Titlebook: Introduction to Markov Chains; With Special Emphasi Ehrhard Behrends Textbook 2000 Springer Fachmedien Wiesbaden 2000 Counting.Finite.Marko

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厚颜

Advanced Lectures in Mathematicshttp://image.papertrans.cn/i/image/473862.jpg

审问

可触知

Transient statesAs in the preceding chapter we fix a Markov chain on a finite state space .. The notation will be as before: ..,..., .. are the minimal closed sets, and . := . (.. U ... U ..).

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An analytical lemmaLet . = (.., .., ...) and . = (.., .., ...) be real sequences. Their . is defined to be the sequence ..

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Perron-Frobenius theoryIn this chapter we aim at understanding why the . of the transition matrix . of a chain play a fundamental role for the rate of convergence to the equilibrium distribution. Also we will discuss some other far-reaching algebraic consequences of the fact that a square matrix is stochastic..

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esculent

Stopping times and the strong Markov propertyThis chapter prepares our investigations of how . can be used to bound mixing rates, it also will be of importance in chapter 14.