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On the creative contribution of V. S. Korolyuk to the development of probability theory. (English. Ukrainian original) Zbl 0973.60047

Ukr. Math. J. 52, No. 8, 1161-1178 (2000); translation from Ukr. Mat. Zh. 52, No. 8, 1014-1030 (2000).
This paper is devoted to the creative contribution of V. S. Korolyuk in the development of the theory of probability and mathematical statistics in connection with his 75th birthday. This paper does not deal with the results of Korolyuk in the problems of cybernetics and in the applied aspects of his activity. The paper contains five sections: Asymptotical analysis in the boundary problems for random walks and Poisson processes; Potential method in the boundary problems for processes with independent increments and random walks; Boundary problems for semi-Markov walks on the superposition of two renewal processes; Asymptotical problems for semi-Markov processes and foundations of phase merging; Theory of random evolutions and their applications.

MSC:

60G50 Sums of independent random variables; random walks
60K15 Markov renewal processes, semi-Markov processes
60K05 Renewal theory
60G51 Processes with independent increments; Lévy processes
60J50 Boundary theory for Markov processes

Citations:

Zbl 0973.60046
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