Page 627 - Probability and Statistical Inference

604 14. Appendix

ting some independent project in the assigned field. Before the final examina-
tions, Kolmogorov submitted fourteen original research papers written in the
required fields. Buried in these papers, there were new discoveries which
included some of his fundamental contributions on the Strong Law of Large
Numbers, the Central Limit Theorem, and the Law of the Iterated Logarithm.
His 1931 paper, Markov Processes with Continuous States in Continuous Time,
laid the foundation of the stochastic diffusion theory which continues to stand
as a landmark, just like many of Kolmogorov’s other discoveries. We recall
that during 1950-1962, W. Feller broke new grounds on the theory of diffu-
sion and Kolmogorov was delighted.
Kolmogorov’s monograph, Foundations of the Theory of Probability, first
appeared in German in 1933 whose English translation became available in 1950.
This immediately became the manifesto in the axiomatic development in prob-
ability. The world recognizes Kolmogorov as the guiding light and a true pioneer
in probability theory. His 1933 paper on the empirical determination of a distri-
bution has been included in the Breakthroughs in Statistics, Volume II [Johnson
and Kotz (1993)]. Kolmogorov also wrote other important books and mono-
graphs including, Introductory Real Analysis, coauthored with S. V. Fomin (1968
Russian edition, 1970 English edition by Prentice-Hall).
Kolmogorov travelled extensively and enjoyed exchanging ideas with col-
leagues. He energetically listened to anyone around him, young and experi-
enced alike. He had ties with H. Cramér, D. G. Kendall, W. Feller, M. Fréchet,
J. Hadamard, P. Lévy, E. B. Dynkin, J. L. Doob, B. V. Gnedenko, A. Rényi, J.
Neyman, P. C. Mahalanobis, J. B. S. Haldane, Yu. V. Linnik and C. R. Rao,
among others.
Kolmogorov received many honors, including honorary D.Sc. degrees from
the University of Paris, University of Stockholm, Indian Statistical Institute,
and Hungary. He became a foreign member of the Polish Academy of Sci-
ences and the GDR Academy of Sciences, as well as a honorary member of
the London Mathematical Society, the Royal Statistical Society, the Romanian
Academy, and the Hungarian Academy. In 1967, he became a member of the
U. S. National Academy of Sciences.
The two articles, (D. G.) Kendall (1991) and Shiryaev (1991), provide
fascinating commentaries on the life and accomplishments of Kolmogorov.
The article of Shiryaev, the first Ph.D. student and later a close associate
of Kolmogorov, is particularly rich in its portrayal of the human elements.
Kolmogorov enjoyed telling stories and jokes. He also loved mountaineer-
ing, skiing, hiking and swimming. The July 1989 issue of the Annals of
Probability and the September 1990 issue of the Annals of Statistics, both
published by the Institute of Mathematical Statistics, devoted a total of