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Book review

Author(s) Borkar, V.S.
Title Topics in controlled Markov chains
Publisher Longman
Year of publication 1991
Reviewed by Anatoly Zhigljavsky

The monograph exposes the author's results in the field of controlled Markov chains on a countable state space. It can be divided into two parts. In the first part many classical results are rederived basing on the formulation of the control problem as an optimization problem on a suitably defined convex set of "occupation measures". The dynamic programming technique is combined here with ergodic arguments and general convex analysis. The general approach developed in the first part of the book is applied to some specific problems in the second part. Multiobjective control, control under partial observations, parametric non-Bayesian control are the main topics in this part.

The mathematical level of the book is high enough and the presentation is clear.

The topic of the monograph is a bit narrow and it is not suprising that there is no concurrent titles available.

The volume has been produced from the camera ready material with typesetting by a word processor of a low level, ChiWriter is a guess. There is no index, the list of references is quite poor.

Since the price seems to be moderate, the specialists in the area of controlled Markov chains who prefer to read monographs rather than journals are advised to purchase the book. The book might be of certain interest to many researchers in optimization, control and probability theory. Therefore the advise to purchase the book can be extended to the libraries of the institutions connected with the fields.