Stochastic Modelling and Applied Probability

Continuous-Time Markov Chains and Applications

A Two-Time-Scale Approach

Authors: Yin, George, Zhang, Qing

  • 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
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About this book

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.

Reviews

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)


Table of contents (10 chapters)

  • Introduction and Overview

    Yin, G. George (et al.)

    Pages 3-16

  • Mathematical Preliminaries

    Yin, G. George (et al.)

    Pages 17-29

  • Markovian Models

    Yin, G. George (et al.)

    Pages 31-56

  • Asymptotic Expansions of Solutions for Forward Equations

    Yin, G. George (et al.)

    Pages 59-140

  • Occupation Measures: Asymptotic Properties and Ramification

    Yin, G. George (et al.)

    Pages 141-234

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-4346-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4614-4345-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4899-9118-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Continuous-Time Markov Chains and Applications
Book Subtitle
A Two-Time-Scale Approach
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
37
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-4346-9
DOI
10.1007/978-1-4614-4346-9
Hardcover ISBN
978-1-4614-4345-2
Softcover ISBN
978-1-4899-9118-8
Series ISSN
0172-4568
Edition Number
2
Number of Pages
XXII, 430
Topics