Stochastic approximation and recursive algorithms and applications
By: Harold J. Kushner, G. George Yin.
Contributors: Yin, George, 1954-; Kushner, Harold J. 1933-
Series: Applications of mathematics ;; 35
Publisher: Springer
Published: 2003
Place of publication: New York
Language: eng
Number of pages: 474
Subjects: Stochastic approximation; Recursive functions; Algorithms
Description: 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.
Notes: Includes bibliographical references (p. [443]-463) and indexes.
Rev. ed. of: Stochastic approximation algorithms and applications. c1997.