Approximation and Weak Convergence Methods for Random Processes Withapplications to Stochastic Systems Theory

Control and communications engineers, physicists, and probabilitytheorists, among others, will find this book unique. It contains a detaileddevelopment of approximation and limit theorems and methods for random processes andapplies them to numerous problems of practical importance. In particular, itdevelops usable and broad conditions and techniques for showing that a sequ

Control and communications engineers, physicists, and probabilitytheorists, among others, will find this book unique. It contains a detaileddevelopment of approximation and limit theorems and methods for random processes andapplies them to numerous problems of practical importance. In particular, itdevelops usable and broad conditions and techniques for showing that a sequence ofprocesses converges to a Markov diffusion or jump process. This is useful when thenatural physical model is quite complex, in which case a simpler approximation ladiffusion process, for example) is usually made.The book simplifies and extends someimportant older methods and develops some powerful new ones applicable to a widevariety of limit and approximation problems. The theory of weak convergence ofprobability measures is introduced along with general and usable methods (forexample, perturbed test function, martingale, and direct averaging) for provingtightness and weak convergence.Kushner's study begins with a systematic developmentof the method. It then treats dynamical system models that have state-dependentnoise or nonsmooth dynamics. Perturbed Liapunov function methods are developed forstability studies of nonMarkovian problems and for the study of asymptoticdistributions of non-Markovian systems. Three chapters are devoted to applicationsin control and communication theory (for example, phase-locked loops and adoptivefilters). Smallnoise problems and an introduction to the theory of large deviationsand applications conclude the book.Harold J. Kushner is Professor of AppliedMathematics and Engineering at Brown University and is one of the leadingresearchers in the area of stochastic processes concerned with analysis andsynthesis in control and communications theory. This book is the sixth in The MITPress Series in Signal Processing, Optimization, and Control, edited by Alan S.Willsky.