Vladimir Semenovich Korolyuk (on his 75th birthday) (Q2722132)

This notice is devoted to the short scientific biography of Academician V. S. Korolyuk. He was born 19.08.1925 in Kiev, Ukraine, where he graduated from the secondary school. Being on military service, he had finished the first two years by correspondence at Kharkiv University, Ukraine. He continued his study at Kyiv State University in 1947. He graduated in 1950. Scientific interests of V. S. Korolyuk were formed under the influence of Academician B. V. Gnedenko. In his M. Sc. diploma (under supervision of B. V. Gnedenko) V. S. Korolyuk gave more precisely a description of the attraction fields of stable laws of distributions and well grounded the conditions of attraction in terms of characteristic functions. He started post-graduate study (under supervision of B. V. Gnedenko) at the Institute of Mathematics of the Academy of Sciences of Ukraine (ASU) in 1951 and continued his post-graduate study at Moscow University. He defended his Candidate of Math. and Phys. Sci. thesis ``On Kolmogorov-Smirnov test'' in 1954. Under the influence of O. Ya. Khinchin he developed new methods in queueing theory and applied them to the proof of the famous theorem on the equality of intensity of stationary input and its parameter (``Korolyuk theorem''). From 1954 V. S. Korolyuk is a permanent collaborator at the Institute of Mathematics of the ASU. He was head of the theory of probability and mathematical statistics department (1960-1995). He defended his Doctor Math. and Phys. Sci. thesis ``Asymptotical analysis in the boundary problems of random walks'' in 1963. From 1966 to 1988 V. S. Korolyuk was Executive Director of the Institute of Mathematics. From 1967 he was a corresponding member of the ASU and since 1976 he is Academician of the ASU. NEWLINENEWLINENEWLINEStudy of boundary problems in the frame of asymptotic analysis started in the 1960s V. S. Korolyuk continued with his pupils (D. V. Gusak, M. S. Bratijchuk, and others) with application of factorization identities to random walks and developed the potential method for semi-continuous random walks and processes with independent increments. The results of these studies were published in his monograph [\textit{V. S. Korolyuk}, Boundary problems for compound Poisson processes. Kiev: Naukova Dumka. (1975; Zbl 0329.60040)] and in the monograph [\textit{V. S. Korolyuk, M. S. Bratijchuk} and \textit{B. Pirdzhanov} , Boundary problems for random walks. Ashkhabad Ylum 257 p. (1987)]. NEWLINENEWLINENEWLINEV. S. Korolyuk initiated in Ukraine the new direction in the theory of semi-Markov processes -- theory of asymptotic phase averaging and merging of random processes. Results of investigation were published in the monographs [\textit{V. S. Korolyuk} and \textit{A. F. Turbin}, Semi-Markov processes and their applications. Kiev: Naukova Dumka. 181 p. (1976; Zbl 0371.60106); \textit{V. S. Korolyuk} and \textit{A. F. Turbin}, Mathematical principles for phase extension of complex systems. Kiev: Naukova Dumka. 219 p. (1978; Zbl 0411.60003)]. NEWLINENEWLINENEWLINEIn the end of 1970s, Korolyuk and Yu. V. Borovskich started the investigation of problems of mathematical statistics in the frame of approximation of distributions. On the base of the theory of random permanents -- created by them -- they developed the new approach to the theory of symmetrical \(U\)-statistics and order statistics. Results of these investigations were published in their monographs [\textit{V. S. Korolyuk} and \textit{Yu. V. Borovskikh}, Analytic problems of the asymptotic behavior of probability distributions. Kiev: Naukova Dumka. (1981; Zbl 0541.60017); \textit{V. S. Korolyuk} and \textit{Yu. V. Borovskikh}, Theory of \(U\)-statistics. Mathematics and its Applications (Dordrecht). 273. Dordrecht: Kluwer Academic Publishers. (1994; Zbl 0785.60015); \textit{V. S. Korolyuk} and \textit{Yu. V. Borovskikh }, Random permanents. Utrecht: VSP. (1994; Zbl 0845.60020)] and others. NEWLINENEWLINENEWLINEIn the end of the 1980s, Korolyuk started to study problems related to the asymptotical analysis of random evolutions. The results of this direction were developed and summarized in the monographs [\textit{V. S. Korolyuk} and \textit{A. V. Swishchuk}, Semi-Markov random evolutions. Mathematics and its Applications (Dordrecht). 308. Dordrecht: Kluwer Academic Publishers. (1994; Zbl 0813.60083); \textit{V. S. Korolyuk} and \textit{A. V. Swishchuk}, Evolution stochastic systems. Averaging algorithms and diffusion approximation. Kyiv: Instytut Matematyky NAN Ukrainy. 344 p. (2000)]. NEWLINENEWLINENEWLINEV. S. Korolyuk has had 40 Cand. Math. and Phys. Sci. as his pupils, among them about 20 are Doctor of Math. and Phys. Sci. His mathematical legacy includes 300 papers and 30 monographs.