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Methodol Comput Appl Probab (2015) 17:514 DOI 10.1007/s11009-013-9353-8
B.V. Gnedenko: Classic of Limit Theorems in the Theory of Probability
Volodymyr S. Koroliuk
Received: 17 October 2012 / Revised: 21 May 2013 / Accepted: 18 June 2013 / Published online: 9 July 2013 Springer Science+Business Media New York 2013
Abstract B.V. Gnedenko is an outstanding scientist-mathematician, who worked in the area of probability theory and its applications. B.V. Gnedenko deserved worldwide popularity by his investigations of limit distributions for sums of independent random variables (Gnedenko and Kolmogorov 1954) that completed a long period of probability theory development up to the middle of XX-th century. The main idea of accompanied infinitely divisible distributions developed by B.V. Gnedenko, became a guidance in the limit theory of semimartingales as it is presented by Jacod and Shiryaev (1987) and others (inlar et al. 1980). The triplet of predictable characteristics for semimartingale is the main idea in investigation the limit behavior for the random evolutions in the scheme of Poisson approximation (Koroliuk and Limnios, Theory Probab Appl 49(4):629644, 2005b).
Keywords B.V. Gnedenko Limit theorem Process with independent increments
Poisson approximation
AMS 2000 Subject Classications MSC 01A60 MSC 60F05
1 Introduction
After the end of the World War II in Europe, namely in May 1945, the Soviet Government sent young talented scientists to western regions of Ukraine for creation of favourable conditions for the development of science and culture. B.V. Gnedenko (Lviv University) and N.N. Bogoliubov (Chernivtsi University) were among them.
Boris Vladimirovich organized a chair of probability theory and founded a seminar. His first Ukrainian students appeared, namely O.S. Parasiuk, E.L. Rvacheva, Mejzler and others. At the end of 1949, Boris Vladimirovich moved to Kyiv and
V. S. Koroliuk (B)
Institute of Mathematics NASU, Tereschenkivska str., 3, Kyiv 01601, Ukraine e-mail: [email protected]
6 Methodol Comput Appl Probab (2015) 17:514
created a department of probability theory in the IM and a chair in Kyiv State University. I was lucky! I was prepared to graduate at the faculty of mechanics and mathematics. The only thing I had to do was to choose the subject of my graduation work and prepare its defense. Without any hesitation I decided to take the subject proposed by Boris Vladimirivich. In such a way our creative cooperation...