Stochastic Approximation and Recursive Algorithms and Applications

Harold Kushner

ISBN 10: 0387008942 / ISBN 13: 9780387008943

Verlag: Springer New York Jul 2003, 2003

Beschreibung

Neuware - The basic stochastic approximation algorithms introduced by Robbins and MonroandbyKieferandWolfowitzintheearly1950shavebeenthesubject of an enormous literature, both theoretical and applied. This is due to the large number of applications and the interesting theoretical issues in the analysis of 'dynamically de ned' stochastic processes. The basic paradigm is a stochastic di erence equation such as = + Y , where takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the 'step n size' > 0 is small and might go to zero as n . In its simplest form, n is a parameter of a system, and the random vector Y is a function of n 'noise-corrupted' observations taken on the system when the parameter is set to . One recursively adjusts the parameter so that some goal is met n asymptotically. Thisbookisconcernedwiththequalitativeandasymptotic properties of such recursive algorithms in the diverse forms in which they arise in applications. There are analogous continuous time algorithms, but the conditions and proofs are generally very close to those for the discrete time case. The original work was motivated by the problem of nding a root of a continuous function g ( ), where the function is not known but the - perimenter is able to take 'noisy' measurements at any desired value of . Recursive methods for root nding are common in classical numerical analysis, and it is reasonable to expect that appropriate stochastic analogs would also perform well.

Bestandsnummer des Verkäufers 9780387008943

Bibliografische Details

• Titel: Stochastic Approximation and Recursive Algorithms and Applications
• Verlag: Springer New York Jul 2003
• Erscheinungsjahr: 2003
• Sprache: Englisch
• ISBN-10: 0387008942
• ISBN-13: 9780387008943
• Einband: Buch
• Auflage: 2. Auflage
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.

Von der hinteren Coverseite

 

This revised and expanded second edition presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. There is a complete development of both probability one and weak convergence methods for very general noise processes. The proofs of convergence use the ODE method, the most powerful to date. The assumptions and proof methods are designed to cover the needs of recent applications. The development proceeds from simple to complex problems, allowing the underlying ideas to be more easily understood. Rate of convergence, iterate averaging, high-dimensional problems, stability-ODE methods, two time scale, asynchronous and decentralized algorithms, state-dependent noise, stability methods for correlated noise, perturbed test function methods, and large deviations methods are covered. Many motivating examples from learning theory, ergodic cost problems for discrete event systems, wireless communications, adaptive control, signal processing, and elsewhere illustrate the applications of the theory.