Stochastic Modelling and Applied Probability

Continuous-Time Markov Chains and Applications

A Singular Perturbation Approach

Authors: Yin, George G., Zhang, Qing

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About this book

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 nonstationary cases have been treated in the literature, much emphasis has been on stationary Markov chains and their basic properties such as ergodicity, recurrence, and stability. In contrast, this book focuses on singularly perturbed nonstationary Markov chains and their asymptotic properties. Singular perturbation theory has a long history and is a powerful tool for a wide variety of applications.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-1-4612-0627-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Continuous-Time Markov Chains and Applications
Book Subtitle
A Singular Perturbation Approach
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
37
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0627-9
DOI
10.1007/978-1-4612-0627-9
Series ISSN
0172-4568
Edition Number
1
Number of Pages
XV, 351
Topics