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Book review

Author(s) Stroock, Daniel. W.
Title Probability Theory (An analytic view)
Publisher Cambridge University Press
Year of publication 1993
Reviewed by Mihai Postolache

The concept of probability occurs in almost all scientific disciplines ranging from applied and theoretical physics to queuing theory, games theory, biology. The theory underlying probability has been approached from numerous points of view, the axiomatic approach has proved to be the most successful. This approach is used by Professor Stroock in the present volume.

This book is a lucid presentation of some advanced concepts in probability including eight chapters, an appendix with notations, preface, index, table of contents sufficiently detailed. No bibliography but interesting footnotes are presented. Each chapter contains interesting applied exercises and problems which allow the reader to understand some results. This volume is suitable for an advanced course on probability covering both elementary notions about the independent random variables, the central limit theorem, convergence of probability measure together important examples as well as more specialized notions such that Wiener's measure, martingales and potential theory. The material is organized so as to introduce as soon as possible these concepts.

Probability Theory is a graduate level book for scientists or researchers and may be recommended as a supplementary text. Containing a deeply but coherent treatment of various concepts, the book can be used with advantage by prospective mathematicians from universities.

Intended to attract readers interested both in theory and applications the book furnishes interrelations with the diffusion processes, evolution equations solving and another applications. This research level book is very well written all concepts being clearly presented. The stated results include complete proofs.

In my opinion, this major material provides a good introduction to the stated subject. The book being very high specialized is designed mainly for the institutional market and for individuals with a sound background in mathematics.