Cambridge Notes About Markov chains

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These notes contain material prepared by colleagues who have also presented this course at Markov chains..pdf (703.25 KB, 需要: 25 个论坛币)

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, especially James Norris. The material mainly comes from books of Norris, Grimmett & Stirzaker, Ross, Aldous & Fill, and Grinstead & Snell. Many of the examples are classic and ought to occur in any sensible course on Markov chains.


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关键词：Cambridge bridge Chains Markov About Cambridge University Markovchains

Contents
Table of Contents i
Schedules iv
1 Definitions, basic properties, the transition matrix
2 Calculation of n-step transition probabilities, class structure, absorption, and irreducibility
3 Hitting probabilities and mean hitting times
4 Survival probability for birth and death chains, stopping times and strong Markov property
5 Recurrence and transience
6 Random walks in dimensions one, two and three
7 Invariant distributions 25 7.1 Examples of invariant distributions
8 Existence and uniqueness of invariant distribution, mean return time, positive and null recurrence
9 Convergence to equilibrium for ergodic chains
10 Long-run proportion of time spent in given state
11 Time reversal, detailed balance, reversibility, random walk on a graph
12 Concluding problems and recommendations for further study