Titlebook: Continuous-Time Markov Chains and Applications; A Two-Time-Scale App G. George Yin,Qing Zhang Book 2013Latest edition Springer Science+Busi

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Mathematical Preliminaries definitions of stochastic processes and filtrations, which lead to a very important concept in stochastic processes, namely, the notion of martingales. In Section 2.3, we recall the definition of Markov chains. Rather than working exclusively with their transition probabilities, this book concentra

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Asymptotic Expansions of Solutions for Forward Equationsrward equation by means of sequences of functions so that the desired accuracy is reached. As alluded to in Chapter 1, we devote our attention to nonstationary Markov chains with time-varying generators.

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Occupation Measures: Asymptotic Properties and Ramificationhe current chapter is largely probabilistic in nature. The central theme of this chapter is limit results of unscaled as well as scaled sequences of occupation measures, which include the law of large numbers for an unscaled sequence, exponential upper bounds, and asymptotic distribution of a suitab

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Asymptotic Expansions of Solutions for Backward Equationsy distribution vectors. However, in many applications, instead of treating the forward equations, we need to deal with the backward equations. In this chapter, we take a dual point of view by examining the associated backward equations.

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