Stochastic Approximation and Recursive Algorithms and Applications

Harold Kushner

ISBN 10: 0387008942 / ISBN 13: 9780387008943

Edité par Springer New York Jul 2003, 2003

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. N° de réf. du vendeur 9780387008943

Synopsis :

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

Détails bibliographiques

Titre : Stochastic Approximation and Recursive ...
Éditeur : Springer New York Jul 2003
Date d'édition : 2003
Reliure : Buch
Etat : Neu
Edition : 2ème Édition