Continuous-Time Markov Chains and Applications

1. Front Matter

   Pages i-xxi

   PDF

2. Prologue and Preliminaries

   1. Front Matter

      Pages 1-1

      PDF

   2. Introduction and Overview

      • G. George Yin, Qing Zhang

      Pages 3-16

   3. Mathematical Preliminaries

      • G. George Yin, Qing Zhang

      Pages 17-29

   4. Markovian Models

      • G. George Yin, Qing Zhang

      Pages 31-56

3. Two-Time-Scale Markov Chains

   1. Front Matter

      Pages 57-57

      PDF

   2. Asymptotic Expansions of Solutions for Forward Equations

      • G. George Yin, Qing Zhang

      Pages 59-140

   3. Occupation Measures: Asymptotic Properties and Ramification

      • G. George Yin, Qing Zhang

      Pages 141-234

   4. Asymptotic Expansions of Solutions for Backward Equations

      • G. George Yin, Qing Zhang

      Pages 235-257

4. Applications: MDPs, Near-optimal Controls, Numerical Methods, and LQG with Switching

   1. Front Matter

      Pages 259-259

      PDF

   2. Markov Decision Problems

      • G. George Yin, Qing Zhang

      Pages 261-283

   3. Stochastic Control of Dynamical Systems

      • G. George Yin, Qing Zhang

      Pages 285-318

   4. Numerical Methods for Control and Optimization

      • G. George Yin, Qing Zhang

      Pages 319-339

   5. Hybrid LQG Problems

      • G. George Yin, Qing Zhang

      Pages 341-372

5. Back Matter

   Pages 373-427

   PDF

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 to applications 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 edition has 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 the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.

• Markov chains
• continuous-time systems
• probability vectors
• stochastic processes

From the reviews of the second edition:

“This book is the expanded second edition of ‘Continuous-time Markov chains and applications. A singular perturbation approach.’ which appeared 1998. … The book remains clearly of interest to researchers in stochastic control, operation research, manufacturing system, engineering, economics and applied mathematics.” (Michael Högele, zbMATH, Vol. 1277, 2014)

“The book is devoted to a study of continuous time singularly perturbed (SP) Markov chains and their applications in problems of control and optimization. … There is no doubt that this second, revised and updated edition will be also well received by the intended audience (researchers and graduate students in applied mathematics and control engineering interested in modeling and optimization of complex stochastic systems) and will excite further interest to the topic.” (Vladimir Gaitsgory, SIAM Review, Vol. 55 (4), 2013)

• Department of Mathematics, Wayne State University, Detroit, USA

  G. George Yin

• Dept. Mathematics, University of Georgia, Athens, USA

  Qing Zhang

Policies and ethics