Continuous-Time Markov Chains and Applications
Subtitle: A Singular Perturbation Approach
By: by G. George Yin, Qing Zhang
Contributors: Zhang, Qing
Series: Applications of Mathematics, Stochastic Modelling and Applied Probability -- 37; Applications of Mathematics, Stochastic Modelling and Applied Probability -- 37
Publisher: Springer New York
Published: 1998
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 349
ISBN-13: 9781461268444; 9781461206279
Subjects: Mathematics; Mathematical optimization; Distribution (Probability theory)
Description: This is author-approved bcc which should be copy-edited: This book discusses continuous-time Markov chains and applications. Using a singular perturbation approach, it presents a systematic treatment of singularly perturbed systems that naturally arise in queueing theory, control and optimization, and manufacturing systems. It gathers a number of ideas in Markov chains and singular perturbations which are scattered throughout the literature. It presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. The emphasis is on Markov chains with weak and strong interactions and structural properties. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications in controlled dynamic systems, production planning, and numerical methods for control and optimization. It aims at the reduction of dimensionality for problems under Markovian disturbances and provides tools for dealing with large -scale and complex real-world problems. Much of the content is an outgrowth of the authors' recent research. Some of the results have not appeared elsewhere. The book will be an important reference for researchers in applied mathematics, probabilty and stochatic processes, operations research, control theory, and optimization.
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Table of contents: title: Prologue and Preliminaries: Introduction and overview- Mathematical preliminaries. Markovian models; title: Singularly perturbed Markov chains: Asymptotic expansion: Irreducible generators. Asymptotic normality and exponential bounds. Asymptotic expansion: Weak and strong interactions. Weak and strong interactions: Asymptotic properties and ramification; title: Optimizations and numerical methods: Markov decision problems. Stochastic control of dynamical systems. Numerical methods for control and optimization.