Stochastic Approximation Cambridge Tracts in Mathematics Series

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields.

Preface; 1. Introduction; 2. The Robbins-Monro method; 3. The Kiefer-Wolfowitz method; 4. Applications; 5. Multivariate stochastic-approximation methods; 6. Asymptotic normality; 7. The approximation for continuous random processes; 8. Up-and-down method; Appendices; Bibliography; Index.