Continuous-Time Markov Chains and Applications
Subtitle: A Two-Time-Scale Approach
By: by G. George Yin, Qing Zhang
Contributors: Zhang, Qing; SpringerLink (Online service)
Edition: 2nd ed. 2013.
Series: Stochastic Modelling and Applied Probability -- 37
Publisher: Springer New York; Imprint: Springer
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 427
ISBN-13: 9781461443469
Subjects: Probability Theory and Stochastic Processes; Distribution (Probability theory); Calculus of Variations and Optimal Control; Optimization; Appl.Mathematics/Computational Methods of Engineering; Engineering mathematics; Management Science Operations Research; Mathematics; Mathematical optimization
Description: <p>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.</p><p><br>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. <br><br></p>
Table of contents: title: <p>​<b> Prologue and Preliminaries</b>: Introduction and overview- Mathematical preliminaries; title: Markovian models; title: <b>Two-Time-Scale Markov Chains</b>: Asymptotic Expansions of Solutions for Forward Equations; title: Occupation Measures: Asymptotic Properties and Ramification; title: Asymptotic Expansions of Solutions for Backward Equations; title: <b>Applications:MDPs, Near-optimal Controls, Numerical Methods, and LQG with Switching: </b>Markov Decision Problems; title: Stochastic Control of Dynamical Systems; title: Numerical Methods for Control and Optimization; title: Hybrid LQG Problems; title: References; title: Index; title: </p>.