Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory (Signal Processing, Optimization, and Control)

Kushner, Harold J.

ISBN 10: 0262110903 / ISBN 13: 9780262110907

Published by Mit Pr, 1984

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Bibliographic Details

• Title: Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory (Signal Processing, Optimization, and Control)
• Publisher: Mit Pr
• Publication Date: 1984
• Language: English
• ISBN 10: 0262110903
• ISBN 13: 9780262110907
• Binding: hardcover
• Condition: Acceptable
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

About this title

Synopsis

Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation (a diffusion process, for example) is usually made.

The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence.

Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of non-Markovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Small-noise problems and an introduction to the theory of large deviations and applications conclude the book.

This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.

About the Author

Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory.