# Dukeedu rick durrett contents 1 markov chains 11

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Unformatted text preview: new ones, email: rtd@math.duke.edu. Rick Durrett Contents 1 Markov Chains 1.1 Deﬁnitions and Examples . . . . . . . . . 1.2 Multistep Transition Probabilities . . . . 1.3 Classiﬁcation of States . . . . . . . . . . . 1.4 Stationary Distributions . . . . . . . . . . 1.5 Limit Behavior . . . . . . . . . . . . . . . 1.6 Special Examples . . . . . . . . . . . . . . 1.6.1 Doubly stochastic chains . . . . . . 1.6.2 Detailed balance condition . . . . . 1.6.3 Reversibility . . . . . . . . . . . . 1.6.4 The Metropolis-Hastings algorithm 1.7 Proofs of the Main Theorems* . . . . . . 1.8 Exit Distributions . . . . . . . . . . . . . 1.9 Exit Times . . . . . . . . . . . . . . . . . 1.10 Inﬁnite State Spaces* . . . . . . . . . . . 1.11 Chapter Summary . . . . . . . . . . . . . 1.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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