马尔科夫链的平稳分布.pdf

发布时间：2022-06-19 发布人：admin 分类：说明书资料大小：1.12M 资料格式：pdf 举报版权申诉

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Main Talk

Stationary Distributions

Fundamental Theorem of Markov Chains

Computing Stationary Distributions

Example: A Simple Queue

Random Walks on Undirected Graphs

Application: An s-t Connectivity Algorithm

Parrondo's Paradox

Outline Markov Chains and Stationary Distributions Matt Williamson1 1Lane Department of Computer Science and Electrical Engineering West Virginia University March 19, 2012 Williamson Markov Chains and Stationary Distributions

Outline Outline 1 Stationary Distributions Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue Williamson Markov Chains and Stationary Distributions

Outline Outline 1 Stationary Distributions Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue 2 Random Walks on Undirected Graphs Application: An s-t Connectivity Algorithm Williamson Markov Chains and Stationary Distributions

Outline Outline 1 Stationary Distributions Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue 2 Random Walks on Undirected Graphs Application: An s-t Connectivity Algorithm 3 Parrondo’s Paradox Williamson Markov Chains and Stationary Distributions

Stationary Distributions Random Walks on Undirected Graphs Parrondo’s Paradox Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue Outline 1 Stationary Distributions Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue 2 Random Walks on Undirected Graphs Application: An s-t Connectivity Algorithm 3 Parrondo’s Paradox Williamson Markov Chains and Stationary Distributions

Stationary Distributions Random Walks on Undirected Graphs Parrondo’s Paradox Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue Probability Matrix Recall Let P be a one-step probability matrix of a Markov chain such that  P = P0,0 P0,1 P1,0 P1,1 ... ... Pi,1 Pi,0 ... ... · · · P0,j · · · P1,j ... ... · · · Pi,j ... ... · · · · · · ... · · · ...  . Williamson Markov Chains and Stationary Distributions

Stationary Distributions Random Walks on Undirected Graphs Parrondo’s Paradox Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue Probability Matrix Recall Let P be a one-step probability matrix of a Markov chain such that  P = P0,0 P0,1 P1,0 P1,1 ... ... Pi,1 Pi,0 ... ... · · · P0,j · · · P1,j ... ... · · · Pi,j ... ... · · · · · · ... · · · ...  . Let ¯p(t) = (p0(t), p1(t), p2(t), . . . ) be the vector giving the probability distribution of the state of the chain at time t. Williamson Markov Chains and Stationary Distributions

Stationary Distributions Random Walks on Undirected Graphs Parrondo’s Paradox Fundamental Theorem of Markov Chains Computing Stationary Distributions Example: A Simple Queue Probability Matrix Recall Let P be a one-step probability matrix of a Markov chain such that  P = P0,0 P0,1 P1,0 P1,1 ... ... Pi,1 Pi,0 ... ... · · · P0,j · · · P1,j ... ... · · · Pi,j ... ... · · · · · · ... · · · ...  . Let ¯p(t) = (p0(t), p1(t), p2(t), . . . ) be the vector giving the probability distribution of the state of the chain at time t. Then, ¯p(t) = ¯p(t − 1) · P Williamson Markov Chains and Stationary Distributions

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