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Titlebook: Continuous-Time Markov Chains and Applications; A Singular Perturbat G. George Yin,Qing Zhang Book 19981st edition Springer Science+Busines

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书目名称Continuous-Time Markov Chains and Applications
副标题A Singular Perturbat
编辑G. George Yin,Qing Zhang
视频videohttp://file.papertrans.cn/238/237044/237044.mp4
丛书名称Stochastic Modelling and Applied Probability
图书封面Titlebook: Continuous-Time Markov Chains and Applications; A Singular Perturbat G. George Yin,Qing Zhang Book 19981st edition Springer Science+Busines
描述This book is concerned with continuous-time Markov chains. It develops an integrated approach to singularly perturbed Markovian systems, and reveals interrelations of stochastic processes and singular perturbations. In recent years, Markovian formulations have been used routinely for nu­ merous real-world systems under uncertainties. Quite often, the underlying Markov chain is subject to rather frequent fluctuations and the correspond­ ing states are naturally divisible to a number of groups such that the chain fluctuates very rapidly among different states within a group, but jumps less frequently from one group to another. Various applications in engineer­ ing, economics, and biological and physical sciences have posed increasing demands on an in-depth study of such systems. A basic issue common to many different fields is the understanding of the distribution and the struc­ ture of the underlying uncertainty. Such needs become even more pressing when we deal with complex and/or large-scale Markovian models, whose closed-form solutions are usually very difficult to obtain. Markov chain, a well-known subject, has been studied by a host of re­ searchers for many years. While nonsta
出版日期Book 19981st edition
关键词Markov chain; Probability distribution; Stochastic processes; continuous-time Markov chain; operations r
版次1
doihttps://doi.org/10.1007/978-1-4612-0627-9
isbn_ebook978-1-4612-0627-9Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer Science+Business Media New York 1998
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Hans-Joachim Lauth,Jürgen R. Winkler 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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Verwaltungswissenschaft(en) in Deutschland,ral theme here is on limit results of unscaled as well as scaled sequences of occupation measures, which include law of large numbers for an unscaled sequence, exponential upper bounds, and asymptotic normality of a suitably scaled sequence of occupation times. The study in Chapter 4 is on the proba
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https://doi.org/10.1007/978-3-322-95748-1ecurrent states, the inclusion of absorbing states, and the inclusion of transient states. We have demonstrated that with some modifications, the approach for treating chains with recurrent states can be extended to the other two cases. In view of Remark 6.15 and Remark 6.20, the Markov chain with r
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https://doi.org/10.1007/978-3-322-95789-4it systems that are easier to handle than the original problems. The optimal or nearly optimal controls of the limit problems can be used to construct nearly optimal controls of the original systems. Although the limit systems are substantially simpler than the original pre-limit ones, closed-form s
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