Overview
- Authors:
-
-
G. George Yin
-
Department of Mathematics, Wayne State University, Detroit, USA
-
Qing Zhang
-
Department of Mathematics, University of Georgia, Athens, USA
Access this book
Other ways to access
Table of contents (10 chapters)
-
-
Prologue and Preliminaries
-
-
- G. George Yin, Qing Zhang
Pages 3-14
-
- G. George Yin, Qing Zhang
Pages 15-24
-
- G. George Yin, Qing Zhang
Pages 25-50
-
Singularly Perturbed Markov Chains
-
-
- G. George Yin, Qing Zhang
Pages 53-78
-
- G. George Yin, Qing Zhang
Pages 79-109
-
- G. George Yin, Qing Zhang
Pages 111-166
-
- G. George Yin, Qing Zhang
Pages 167-217
-
Control and Numerical Methods
-
Front Matter
Pages 219-219
-
- G. George Yin, Qing Zhang
Pages 221-242
-
- G. George Yin, Qing Zhang
Pages 243-276
-
- G. George Yin, Qing Zhang
Pages 277-298
-
Back Matter
Pages 299-351
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.
Authors and Affiliations
-
Department of Mathematics, Wayne State University, Detroit, USA
G. George Yin
-
Department of Mathematics, University of Georgia, Athens, USA
Qing Zhang
