Continuous-Time Markov Chains and Applications [electronic resource] : A Two-Time-Scale Approach / by G. George Yin, Qing Zhang.Material type: TextSeries: Stochastic Modelling and Applied Probability ; 37Publisher: New York, NY : Springer New York : Imprint: Springer, 2013Edition: Second editionDescription: XXII, 430 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781461443469Subject(s): 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 EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access online
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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.-.
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.