Four Areas of Yu. V. Prokhorov's Studies and Their Perspectives

Abstract

Research areas of Yu. V. Prokhorov and his school in the 1999--2013 time period are presented. In these studies several problems of the theory of probability, where the uniform distribution is the target limiting or initial distribution, have been solved. A number of moment inequalities for classical distributions are established. Based on generalized moment identities, new methods for solving the linearization problem for polynomials orthogonal with respect to classical distributions are elaborated. Some methods for obtaining moment characterizations of probabilistic distributions are suggested as well. Possible ways to extend studies in each of these directions are described.