Stochastic Approximation and Recursive Algorithms and Applications (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
478
Utgivningsdatum
2003-07-01
Upplaga
2nd ed. 2003
Förlag
Springer-Verlag New York Inc.
Medarbetare
Yin, George G.
Illustratör/Fotograf
31 Abb
Illustrationer
XXII, 478 p.
Volymtitel
v. 35
Dimensioner
240 x 160 x 30 mm
Vikt
840 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9780387008943

Stochastic Approximation and Recursive Algorithms and Applications

av Harold Kushner, G George Yin
Inbunden,  Engelska, 2003-07-01
2299
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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.
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Harold Kushner, G George Yin

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From the reviews of the second edition: "This is the second edition of an excellent book on stochastic approximation, recursive algorithms and applications . Although the structure of the book has not been changed, the authors have thoroughly revised it and added additional material ." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1026, 2004) "The book attempts to convince that algorithms naturally arise in many application areas . I do not hesitate to conclude that this book is exceptionally well written. The literature citation is extensive, and pertinent to the topics at hand, throughout. This book could be well suited to those at the level of the graduate researcher and upwards." (A. C. Brooms, Journal of the Royal Statistical Society Series A: Statistics in Society, Vol. 169 (3), 2006)

Innehållsförteckning

Introduction: Applications and Issues.- Applications to Learning, Repeated Games, State Dependent Noise, and Queue Optimization.- Applications in Signal Processing, Communications, and Adaptive Control.- Mathematical Background.- Convergence with Probability One: Martingale Difference Noise.- Convergence with Probability One: Correlated Noise.- Weak Convergence: Introduction.- Weak Convergence Methods for General Algorithms.- Applications: Proofs of Convergence.- Rate of Convergence.- Averaging of the Iterates.- Distributed/Decentralized and Asynchronous Algorithms.

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