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Markov Chain

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Markov Chain

2015-10-28 18:52:58   6  举报

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离散马尔科夫链学习大纲

数学经济学随机过程

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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

Michael Porter Value Chain Template

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Get Started

Michael Porter Value Chain Template

Building the Value Chain

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Get Started

Building the Value Chain

Michael Porter Value Chain Template

 Collect

Get Started

Michael Porter Value Chain Template

Michael Porter Value Chain Template

 Collect

Get Started

Michael Porter Value Chain Template

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