Harold J. Kushner | Akateeminen Kirjakauppa

The book 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, with which the asymptotic behavior
is characterized by the limit behavior of a mean ODE. 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, general correlated and state-dependent noise, perturbed
test function methods, and large devitations methods, are covered.
Many motivational examples from learning theory, ergodic cost problems
for discrete event systems, wireless communications, adaptive control,
signal processing, and elsewhere, 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.
Harold J. Kushner is a University Professor and Professor of Applied
Mathematics at Brown University. He has written numerous books and
articles on virtually all aspects of stochastic systems theory, and
has received various awards including the IEEE Control Systems Field
Award. TOC:Introduction: Applications and Issues.- Applications to Learning, Repeated Games, State Dependent Noise, and Queue Optimization.- Applications to Signal Processing, Communications, and Adaptive Control.- Mathematical Background.- Convergence w.p.1: Martingale Difference Noise.- Convergence w.p.1: 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