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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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书目名称Continuous-Time Markov Chains and Applications
副标题A Two-Time-Scale App
编辑G. George Yin,Qing Zhang
视频video
概述New chapters added on backward equations and LQG control problems.Bridges the gap between theory and applications.Presents results on asymptotic expansions of the corresponding probability distributio
丛书名称Stochastic Modelling and Applied Probability
图书封面Titlebook: Continuous-Time Markov Chains and Applications; A Two-Time-Scale App G. George Yin,Qing Zhang Book 2013Latest edition Springer Science+Busi
描述This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted toapplications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second editionhas been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified.This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from th
出版日期Book 2013Latest edition
关键词Markov chains; continuous-time systems; probability vectors; stochastic processes
版次2
doihttps://doi.org/10.1007/978-1-4614-4346-9
isbn_softcover978-1-4899-9118-8
isbn_ebook978-1-4614-4346-9Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer Science+Business Media, LLC 2013
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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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