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Book review

Author(s) Kolmogorov, A.N.
Title Selected Works of A.N. Kolmogorov, Volume II: Probability theory and Mathematical statistics
Publisher Kluwer
Year of publication 1992
Reviewed by Jordan Stoyanov

[This volume edited by A.N. Shiryaev]

From several points of view the present volume (like vol. I and III) is unusual as well as unique in the world scientific literature. There is no necessity to write about the fundamentality of the contributions of A.N. Kolmogorov and especially when discussing on Probability and Mathematical statistics. The volume includes 53 articles covering a broad spectrum of topics. The selection of the articles was done by A.N. Kolmogorov himself. It is curious to mention that the first of the articles was published 1925 while the last one appeared 1983. Also, almost all articles have been originally published either in German, or in French, or in Italian, or in Russian. Some of them appear now in English for first time.

When reading the papers of A.N. Kolmogorov we discover again how deeply every notion is motivated and how strongly every result is justified. It is surprising to realize that there are too many ideas and techniques created by Kolmogorov more than 50 years ago which are in use today without any changes. This happens very rarely but only the great scientist and masters can do it. The range of topics treated in the articles is so wide: from convergence of random series and limit theorems, through Markov, Gaussian and stationary processes, to logical foundation of probability theory. Important topics of mathematical statistics are considered. A reasonable number of papers are devoted to problems in other fields: biology, physics.

In the end of the volume we find quite interesting commentaries of A.N. Kolmogorov on his own old results. Additionally, leading experts in the field (A. Skorohod, Yu. Rozanov, B. Sevastyanov, V. Zolotarev, A. Yushkevich, A. Yaglom, A. Wentzell, Yu. Belyaev, A. Novikov, and others) have written very useful surveys on many developments started by Kolmogorov. Thus the English speaking reader has finally the rare chance for a direct acquantance with the contributions of one of the greatests mathematicians of our centery.

There is no doubt that this volume, like the other ones, will be met with a great interest by scientists working in both the theoretical stochastics and its numerous applications. This volume will be a substancial addition to the collection of any institutional library, despite the higher price. Surely many scientist will find absolutely deserving to have their own personal copies.

Once again: Do not miss your rare chance to read one of the greatests masters and the teacher of everyone of us.