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...

This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production...