Approximation and Weak Convergence Methods for Random Processes (Paperback)

• Category:  Books  »  Mathematics  »  Probability & Statistics - General
• Format: Paperback   Learn more about the Paperback format using Tower WIKI.
• Publisher: Mit Press
• Number of Pages: 292
• ISBN: 0262512181
• WAPI (Tower ID): 112937058
• Release Date: April 26, 1984
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• Tower.com Sales Rank: #1032469 in Books (See Top 100 Books Bestsellers)
• #10337 in Mathematics (See Top 100 Mathematics Bestsellers)
• #1696 in Probability & Statistics - General (See Top 100 Probability & Statistics - General Bestsellers)

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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 la 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 nonMarkovian 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). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area ofstochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.

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