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Book review

Author(s) Ljung, L.
Pflug, G.
Walk, H.
Title Stochastic approximation and optimization of random systems
Publisher Birkhäuser
Year of publication 1992
Reviewed by Anatoly Zhigljavsky

The book provides a short course of the stochastic approximation and its applications. The main topics are the almost sure convergence of stochastic approximation algorithms, rate of convergence, especially invariance principles, optimization under stochastic constraints, and control of stochastic systems.

The authors are well-known authorities in the field. Therefore as was expected the book is professionally written. It contains both all the necessary proofs and a lot of information per page. The book resulted from the lectures that had been given by the authors in a seminar organized by the German Mathematical Society. The quality of publishing is good.

The mathematical level is quite high. The prerequisites for reading the book are basic knowledge in probability, mathematical statistics, and optimization. The book could be useful for both students of mathematical and some engineering specialities as a text book on stochastic approximation and for specialists in optimization as a reference book. Since most of the applications described are from signal processing and identification, the book might also be of interest for researches in this field.

Purchase of the book would be a good investment by those working in the fields of stochastic optimization and signal processing. It is also worthwhile to buy the book for many university libraries with the aim to use it for the purpose of training.