Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory

Download Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory

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 of stochastic 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.
Stochastic Approximation and Recursive Algorithms and Applications

Author: Harold Kushner
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
In recent years algorithms of the stochastic approximation type have found applications in new and diverse areas, and new techniques have been developed for proofs of convergence and rate of convergence. The actual and potential applications in signal processing have exploded. New challenges have arisen in applications to adaptive control. This book presents a thorough coverage of the ODE method used to analyze these algorithms.
Handbook of Stochastic Analysis and Applications

An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.