Continuous-Time Markov Chains and Applications
A Two-Time-Scale Approach
Yin, G. George.
creator
author.
Zhang, Qing.
author.
SpringerLink (Online service)
text
xxu
2013
Second edition.
monographic
eng
access
XXII, 430 p. online resource.
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.
Prologue and Preliminaries: Introduction and overview- Mathematical preliminaries -- Markovian models -- Two-Time-Scale Markov Chains: Asymptotic Expansions of Solutions for Forward Equations -- Occupation Measures: Asymptotic Properties and Ramification -- Asymptotic Expansions of Solutions for Backward Equations -- Applications:MDPs, Near-optimal Controls, Numerical Methods, and LQG with Switching: Markov Decision Problems -- Stochastic Control of Dynamical Systems -- Numerical Methods for Control and Optimization -- Hybrid LQG Problems -- References -- Index.-.
by G. George Yin, Qing Zhang.
Mathematics
Calculus of variations
Operations research
Management science
Probabilities
Applied mathematics
Engineering mathematics
Mathematics
Probability Theory and Stochastic Processes
Calculus of Variations and Optimal Control; Optimization
Operations Research, Management Science
Appl.Mathematics/Computational Methods of Engineering
QA273.A1-274.9
QA274-274.9
519.2
Springer eBooks
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