Méthodes récursives aléatoires. (Recursive stochastic methods). (French) Zbl 0703.62084

Techniques Stochastiques. Paris etc.: Masson. xiv, 359 p. FF 289.00 (1990).
The remarkable development of computational techniques has brought about to an exceptional success of recursive methods. The present book, devoted to random methods of this type, is written in French with clarity and precision and is intended to readers with basic (although advanced) notions of probability and statistics for theoretical rather than practical use.
The topics covered are: Univariate and multivariate (martingales, regression, linear models) recursive methods, rates of convergence, stability (autoregressive models, Markov chains, nonlinear models and estimation, Markovian representations), identification of linear models, control (controlled and stabilized models, controlled iterative models, tracking), recurrence (Markov chains, rates of convergence to the stationary distribution), learning. Each section ends with bibliographical notes and comments; the book’s bibliography contains only basic references.
A forthcoming English version of this book, adapted and revised to meet the needs of graduate students, will certainly be a welcome addition to the literature.
Reviewer: R.Theodorescu


62L99 Sequential statistical methods
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
93E99 Stochastic systems and control
62L20 Stochastic approximation
65C99 Probabilistic methods, stochastic differential equations