Continuous-Time Markov Chains and Applicat...

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Beschreibung

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.

Zusammenfassung

New chapters added on backward equations and LQG control problems

Bridges the gap between theory and applications

Presents results on asymptotic expansions of the corresponding probability distributions

Inhaltsverzeichnis

¿ 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.-

Details

Erscheinungsjahr:	2012
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Stochastic Modelling and Applied Probability
Inhalt:	xxii 430 S.
ISBN-13:	9781461443452
ISBN-10:	1461443458
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Zhang, Qing Yin, G. George
Auflage:	2nd ed. 2013
Hersteller:	Springer New York Springer US, New York, N.Y. Stochastic Modelling and Applied Probability
Maße:	241 x 160 x 28 mm
Von/Mit:	Qing Zhang (u. a.)
Erscheinungsdatum:	25.10.2012
Gewicht:	0,84 kg