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STOCHASTIC SYSTEMS IN MERGING PHASE SPACE

by Vladimir S Koroliuk (National Academy of Sciences, Ukraine) & Nikolaos Limnios (University of Technology of Compiègne, France)

Table of Contents (123k)
Chapter 1: Markov and Semi-Markov Processes (835k)

This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models.

The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book.


Contents:

  • Markov and Semi-Markov Processes
  • Stochastic Systems with Switching
  • Stochastic Systems in the Series Scheme
  • Stochastic Systems with Split and Merging
  • Phase Merging Principles
  • Weak Convergence
  • Poisson Approximation
  • Applications
  • Appendices:
  • Weak Convergence of Probability Measures
  • Some Limit Theorems for Stochastic Processes
  • Some Auxiliary Results


Readership: Post-graduate students, teachers and researchers, as well as engineers dealing with the simplification of complex systems.


“Introductory facts related to weak convergence of the stochastic process and the convergence of semimartigales, theorems, generalizations for results previously published by the authors, proofs and applications are well organized and distributed throughout nine chapters and three appendices.”

Mathematical Reviews





“This book may serve as a textbook for graduate students, postdoctoral seminars or courses for applied scientists and engineers in stochastic approximation of complex systems: queueing, reliability, risk, finance.”

Zentralblatt MATH




348pp Pub. date: Dec 2005
ISBN 978-981-256-591-4
981-256-591-4
US$89 / £48


Copyright © 2008 World Scientific Publishing Co. All rights reserved.
Updated on 4 July 2008