Markov Chain
2015-10-28 18:52:58 4 举报AI智能生成
离散马尔科夫链学习大纲
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Discrete-time Markov chain
Markov Condition
Strong Markov property
Pij=P(?)
Transaction Matrix
One-step transaction probability
(m-step) transaction probability
Chapman-Kolmogorov equation
Collaps transaction matrix
(Discrete) State Space
States
Communicate
Class property
Regular
存在一个n, 使得从任意i到j的n-step transaction probability 都大于0
Closed
Recurrent
Irreducible
Ergodic
Recurrence Time
Tao_i
Number of times return to state i
Ri
Positive
Null
Transient
Periodic
Aperiodic
Pij
Pij(m)
fii
P(ever return to i when start from i)
fij
\Pi_i
\Mu_i
Mean recurrence time
Nj
Mean time spent in transient states
Mtt=(I-Ptt)^(-1)
Proof
Shiryaev
(Xn) has an unique stationary distribution
Existence of limiting distribution of (Xn)
Exactly one positive recurrent class
Time reversible Markov chain
Definition
Property
Pi_iPij=Pi_jPji
Proof
(Time-homogeneous)
Continuoes-time Markov chain
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