Teorema mengenai Limiting Probability dan Irreducible

<p style="text-align: left; margin-left: 48px; line-height: 19px; font-weight: bold;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Teorema mengenai Limiting Probability</span></p><p style="text-align: left; margin-left: 48px; line-height: 19px;"><span style="font-size: 12pt; color: rgb(0, 0, 0);">Definisi: </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">j</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁾</span>}</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">adalah probabilitas suatu rantai Markov {</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">} berad</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">a </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dalam status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> pada step ke </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. Maka, </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">j</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁾</span>}</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">]</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">Distribusi awal (intial) dari masing-masing status 0, 1, 2, .. dinyataka</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">n </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">sebagai</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽⁰⁾</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">0</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">], untuk j = 0, 1, 2, …</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="text-align: left; margin-bottom: 45px; margin-left: 48px; line-height: 20px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Suatu rantai Markov memiliki distribusi probabilitas stasioner</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">(π</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">0</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">1</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">2</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, …, </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">) apabila terpenuhi persamaan</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π =π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">asalkan setiap </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">≥ </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">0 dan </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 18pt; color: rgb(0, 0, 0);">_∑</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_i</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_i</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">= </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">1</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Jika suatu rantai Markov homogen waktu (stasioner dari waktu k</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">e </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">aktu) yang irreducible, aperiodic, maka limit probabilita</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">s </span></p> <p style="text-align: left; margin-bottom: -12px; margin-left: 118px;"> <span style="font-size: 7pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 7pt; color: rgb(0, 0, 0);">)</span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px;"> <span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">_j</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">= </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">lim</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">_j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, untuk </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = 0, 1, … </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 84px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 7pt; color: rgb(0, 0, 0);">→∞ </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">selalu ada dan independen dari distribusi probabilitas status awal </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽⁰⁾</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= </span></p> <p style="text-align: left; margin-bottom: -12px; margin-left: 67px;"> <span style="font-size: 8pt; color: rgb(0, 0, 0);">(0)(0)</span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 8pt; color: rgb(0, 0, 0);">0</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">, π</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 8pt; color: rgb(0, 0, 0);">1</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">,π</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 8pt; color: rgb(0, 0, 0);">2</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽⁰⁾</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, ….)</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">Jika seluruh status tidak positive recurrent (jadi seluruhnya recurren</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">t </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">null atau seluruhnya transient), maka </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">π</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">j </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= 0 untuk semua </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dan tida</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">k </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">terdapat distribusi probabilitas stasioner</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">.<br /></span></p><p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"><span style="font-size: 12pt; color: rgb(0, 0, 0);"><br /></span></p><p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"><span style="font-weight: bold;">Teorema mengenai Irreducible </span><br /><span style="font-size: 12pt; color: rgb(0, 0, 0);"></span></p><p style="text-align: left; margin-left: 48px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Jika {</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">} suatu rantai Markov, maka tepat salah satu kondisi berikut ini terjadi 1) Semua status adalah positive recurrent 2) Semua status recurrent null 3) Semua status transient </span></p>

Teorema mengenai Limiting Probability dan Irreducible

Teorema mengenai Limiting ProbabilityDefinisi: πj(n) adalah probabilitas suatu rantai Markov {Xn} berada dalam status j pada step ke n. Maka, πj(n) = P[Xn = j]. Distribusi awal (intial) dari masing…

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Teorema mengenai Relasi Ekovalensi

(a) Relasi i ↔j merupakan relasi ekivalen, yaitu<br /><ol><li> untuk setiap status i, berlaku i ↔ i </li><li>jika i ↔ j , maka juga j ↔ i </li><li>jika i ↔j dan j ↔k maka i ↔ k </li></ol><br />(b) Status-status suatu rantai Markov dapat dipartisi ke dalam kelaskelas ekivalensi sehingga i ↔ j , jika dan hanya jika i dan j berada dalam kelas ekivalensi (partisi) yang sama.<br /><br />(c) Suatu rantai Markov irreducible jika dan hanya jika di dalamnya hanya terdiri atas tepat satu kelas ekivalensi.<br /><br />(d) Jika i ↔ j , maka i dan j memiliki perioda yang sama.<br /><br />(e) Untuk i ↔ j , jika i recurrent maka juga j recurrent.

Teorema mengenai Relasi Ekovalensi

(a) Relasi i ↔j merupakan relasi ekivalen, yaitu untuk setiap status i, berlaku i ↔ i jika i ↔ j , maka juga j ↔ i jika i ↔j dan j ↔k maka i ↔ k (b) Status-status suatu rantai Markov dapat dipartis…

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Terminologi

<p style="text-align: left; margin-left: 96px; text-indent: -47px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Reachable State s</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">tatus </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j reachable </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dari status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">apabila dalam rantai dapat terjadi transisi dari status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> ke status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> melalui sejumlah transisi berhingga; Terdapat </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, 0 </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">≤ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> < </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">∞</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, sehingga </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ij</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> > 0 </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Irreducible Chain </span></p> <p style="text-align: left; margin-left: 96px; line-height: 18px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">jika dalam suatu rantai Markov setiap status reachable dari setiap status lainnya, rantai tersebut adalah </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">irreducible</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Periodic State </span></p> <p style="text-align: left; margin-left: 96px; line-height: 18px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">suatu status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">disebut </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">periodic </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dengan perioda </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">d </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">> 1, jika </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">p</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ii </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">> 0, hanya untuk n = d, 2d, 3d, …; sebaliknya jika </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">p</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ii </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">> 0 untuk </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= 1, 2, 3, … maka status tersebut disebut </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">aperiodic</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Probability Of First Return </span></p> <p style="margin-right: 129px; margin-left: 112px; line-height: 18px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Probabilitas kembali </span><span style="font-size: 12pt; color: rgb(0, 0, 0); text-decoration: underline;">pertama kalinya </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">ke status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">terjadi dalam </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">transisi setelah meninggalkan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">f</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁾</span>}</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">k </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">≠ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> untuk </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">k</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = 1, 2, …, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">-1 | </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">0</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">] (note: </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">f</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽⁰⁾</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> didefinisikan = 1 untuk semua </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">). </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Probability of Ever Return </span></p> <p style="text-align: left; margin-bottom: 8px; margin-left: 96px; line-height: 18px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">probabilitas akan kembalinya ke status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">setelah sebelumnya meninggalkan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 217px; line-height: 9px;"> <span style="font-size: 7pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 7pt; color: rgb(0, 0, 0);">)</span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 144px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">f</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 18pt; color: rgb(0, 0, 0);">_∑</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 7pt; color: rgb(0, 0, 0);">^∞</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">f</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">_i</span></p> <p style="text-align: left; margin-bottom: 33px; margin-left: 190px; line-height: 9px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 7pt; color: rgb(0, 0, 0);">n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 7pt; color: rgb(0, 0, 0);">=</span><span style="font-size: 7pt; color: rgb(0, 0, 0);">1 </span></p> <p style="text-align: left; margin-bottom: 0px;"> <span style="font-size: 6.4pt; color: rgb(0, 0, 0);">¹</span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">Berdasarkan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.4pt; color: rgb(0, 0, 0);">ij </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 6.4pt; color: rgb(0, 0, 0);">¹</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.4pt; color: rgb(0, 0, 0);">ij </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">serta </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 6.4pt; color: rgb(0, 0, 0);">⁰</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.4pt; color: rgb(0, 0, 0);">ij </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">= 1 untuk </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">j </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">dan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 6.4pt; color: rgb(0, 0, 0);">⁰</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.4pt; color: rgb(0, 0, 0);">ij </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">= 0 untuk </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">≠ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 9.9pt; color: rgb(0, 0, 0);">j </span><span style="font-size: 9.9pt; color: rgb(0, 0, 0);">(yaitu Fungsi Delta Kronecker). </span></p> <p style="margin-bottom: 0px; margin-left: 48px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Transient State </span></p> <p style="margin-left: 96px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Suatu status disebut </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">transient </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">jika probabilitas </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">f</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);"><><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">melalui sejumlah transisi terdapat kemungkinan tidak dapat kembali ke </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="margin-bottom: 0px; margin-left: 48px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Recurrent State </span></p> <p style="margin-left: 96px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Suatu status disebut </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">recurrent </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">jika probabilitas </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">f</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= 1; yaitu bahwa setelah dari I melalui sejumlah transisi selalu ada kemungkinan untuk kembali ke </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="margin-bottom: 0px; margin-left: 48px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Mean Recurrence Time of State </span></p> <p style="margin-bottom: 5px; margin-left: 96px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Untuk suatu status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">recurrent</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, jumlah step rata-rata untuk kembali ke status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span></p> <p style="margin-bottom: 0px; margin-left: 135px;"> <span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">∞ </span></p><p style="margin-left: 166px;"> <span style="font-size: 6.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">)</span></p><p style="margin-bottom: 5px; margin-left: 98px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">m</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_i</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 11.9pt; color: rgb(0, 0, 0);">=</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 17.9pt; color: rgb(0, 0, 0);">_∑</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">nf</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_i</span></p> <p style="margin-left: 132px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">=</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">1 </span></p> <p style="margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Null Recurrenct State </span></p> <p style="text-align: center;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Suatu </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">recurrent</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> state disebut </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">reccurent null </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">jika </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">m</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">∞ </span></p> <p style="margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Positive Recurrent State </span></p> <p style="margin-left: 96px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Suatu </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">recurrent </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">state disebut </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">positive reccurent </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">atau </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">recurrent nonnull </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">jika </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">m</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> < </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">∞ </span></p> <p style="margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Communicate State </span></p> <p style="margin-left: 96px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Dua status, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, dikatakan berkomunikasi jika </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">reachable dari </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dan juga </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> reachable dari </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">; ditulis dengan notasi </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">↔ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p> <p style="margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-family: 'sans-serif','TT E 16 E 29 D 8t'; font-size: 12pt; font-weight: bold; color: rgb(0, 0, 0);">Ergodic </span></p> <p style="margin-left: 96px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Rantai Markov disebut ergodic jika </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">irreducible</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">aperiodic</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, dan seluruh status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">positive recurrent</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p>

Terminologi

Reachable State status j reachable dari status i apabila dalam rantai dapat terjadi transisi dari status i ke status j melalui sejumlah transisi berhingga; Terdapat n, 0 ≤ n ∞, sehingga Pnij > 0 Ir…

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Transisi Multistep (n-langkah)

<p style="text-align: left; margin-bottom: 0px; margin-left: 48px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Berdasarkan probabilitas satu langkah di atas, maka dapat dibentuk probabilitas n-langkah (n-step) yang menyatakan probabilitas transisi dari status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> ke status </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> setelah melalui n langkah transisi. </span></p> <p style="text-align: left; margin-left: 98px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ij</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);"> = P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> | </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">0</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">], dengan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = 0, 1, 2, … </span></p> <p style="text-align: left; margin-left: 96px; text-indent: -47px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Untuk rantai Markov dengan probabilitas stasioner mak</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">a </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ij</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);"> = P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n+m</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> | </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">m </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">], dengan </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">m </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">≥ </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">0 </span></p> <p style="text-align: left; margin-bottom: 5px; margin-left: 48px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Sehingga diperoleh</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">¹</span></p> <p style="text-align: left; margin-bottom: -12px; margin-left: 110px; text-indent: 40px; line-height: 9px;"> <span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">∞ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">+</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">m n</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">m </span></p> <p style="text-align: left; margin-bottom: 5px; margin-left: 98px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_ij</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 11.9pt; color: rgb(0, 0, 0);">=</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 17.9pt; color: rgb(0, 0, 0);">_∑</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_ik</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_kj</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> untuk semua </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">m</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">i</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">j </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">≥</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> 0 </span></p> <p style="text-align: left; margin-bottom: 0px; margin-left: 146px; line-height: 9px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">k</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">=</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">0 </span></p> <p style="text-align: left; margin-bottom: 5px; margin-left: 48px; line-height: 19px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Atau secara khusus, </span></p> <p style="margin-bottom: 0px; margin-right: 442px; margin-left: 56px; text-indent: 28px; line-height: 10px;"> <span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">∞ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">nn</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">−</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">1 </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">^P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">ij </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 11.9pt; color: rgb(0, 0, 0);">⁼</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 17.9pt; color: rgb(0, 0, 0);">∑ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">^P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">ik </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">^P</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">k</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">j </span></p> <p style="text-align: left; margin-left: 85px; line-height: 9px;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">k</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">=</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">0 </span></p> <p style="text-align: left; margin-bottom: 5px; margin-left: 48px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Dalam notasi matriks, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁾</span>}</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">adalah matriks transisi untuk multistep, maka dapat </span></p> <p style="text-align: left; margin-bottom: -12px; margin-left: 48px; line-height: 13px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">diperoleh persamaan dalam matriks </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> sb</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">b </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">_P</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">) </span></p> <p style="text-align: left; margin-left: 48px; text-indent: 26px; line-height: 18px;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);"> = </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">^-1)</span>}</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P= P</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">^-2)</span>}</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">PP =… = P</span><span style="font-weight: normal;">^{<span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n </span>}</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">yaitu bahwa </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-weight: normal;">^{<span style="font-size: 8pt; color: rgb(0, 0, 0);">⁽</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">ⁿ</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">⁾</span>}</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> adalah pangkat </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);"> dari matriks </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">. </span></p>

Transisi Multistep (n-langkah)

Berdasarkan probabilitas satu langkah di atas, maka dapat dibentuk probabilitas n-langkah (n-step) yang menyatakan probabilitas transisi dari status i ke status j setelah melalui n langkah transisi. …

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Proses Rantai Markov

<p style="margin-bottom: 0px; margin-left: 48px; text-align: justify;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Proses stokastik {</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">X</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">t</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">), </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">t </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 12pt; color: rgb(0, 0, 0);">∈ </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">T</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">} merupakan suatu Proses Markov jika untuk </span></p><div> </div><p style="margin-bottom: 0px; margin-left: 48px; text-align: justify;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">setiap </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">+1, dengan indeks </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">t</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">1</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">< </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">t</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">2 </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">< …< </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">t</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">< </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">t</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">+1 </span><span style="font-size: 12pt; color: rgb(0, 0, 0);">dan harga-harga status {</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">x</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">1</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">x</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">2</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">, </span></p><div style="text-align: justify;"> </div><p style="margin-bottom: 0px; margin-left: 48px; line-height: 19px; text-align: justify;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">…, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 12pt; color: rgb(0, 0, 0);">x</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 8pt; color: rgb(0, 0, 0);">n</span><span style="font-size: 8pt; color: rgb(0, 0, 0);">+1</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">}, terjadi persamaan</span><span style="font-size: 12pt; color: rgb(0, 0, 0);">: </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">X </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">t</span><span style="font-weight: normal;">_{<span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">₊</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">₁</span>}</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">) = x</span><span style="font-weight: normal;">_{<span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">₊</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">₁</span>}</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">| </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">X </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">t</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">₁</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">) = x</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">₁</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">, </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">X </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">t</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">₂</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">) = x</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">₂</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">,..., </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">X </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">t</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_n</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">) = x</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">_n</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">] </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 11.9pt; color: rgb(0, 0, 0);">= </span></p><div style="text-align: justify;"> </div><p style="margin-bottom: -7px; margin-right: 140px; margin-left: 227px; text-align: justify;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">P</span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">[</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">X </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">t </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">) </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 11.9pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">x </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">| </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">X </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">(</span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">t </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">) </span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 11.9pt; color: rgb(0, 0, 0);">= </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 11.9pt; color: rgb(0, 0, 0);">x </span><span style="font-size: 11.9pt; color: rgb(0, 0, 0);">]</span></p><div style="text-align: justify;"> </div><p style="margin-bottom: 0px; margin-right: 140px; margin-left: 266px; text-align: justify;"> <span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">+</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">1 </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">n</span><span style="font-family: 'sans-serif','TT E 16 E 30 A 0t'; font-size: 6.9pt; color: rgb(0, 0, 0);">+</span><span style="font-size: 6.9pt; color: rgb(0, 0, 0);">1 </span><span style="font-family: 'sans-serif','TT E 16 E 22 B 8t'; font-size: 6.9pt; color: rgb(0, 0, 0);">nn </span></p><div style="text-align: justify;"> </div><p style="margin-left: 48px; line-height: 19px; text-align: justify;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Persamaan tsb. secara narasi dapat dikatakan proses selanjutnya hanya bergantung pada status saat ini, bukan pada “sejarah” dari proses tersebut. Dalam proses Markov status-status proses yang terjadi selama ini dicerminkan oleh status saat ini. </span></p><div style="text-align: justify;"> </div><p style="margin-left: 48px; line-height: 19px; text-align: justify;"> <span style="font-size: 12pt; color: rgb(0, 0, 0);">Sebagaimana terminologi di awal, suatu proses Markov disebut Rantai Markov jika ruang status diskret. Untuk waktu diskret, rantai Markov dapat digambarkan sebagai diagram transisi status. </span></p>

Proses Rantai Markov

Proses stokastik {X(t), t ∈ T} merupakan suatu Proses Markov jika untuk setiap n+1, dengan indeks t1t2 tn tn+1 dan harga-harga status {x1, x2, …, xn+1}, terjadi persamaan: P[X (tn+1) = xn+1| X (…

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