To the history of Saint-Petersburg school of Probability and Statistics. II. Random processes and dependent variables

Abstract

This is the second article in a series of surveys devoted to the scientific achievements of the Leningrad— Saint-Petersburg school of Probability and Statistics during the period from 1947 to 2017. It is devoted to the works on limit theorems for dependent variables, in particular Markov chains, mixing sequences, the sequences admitting a martingale approximation, and to various topics in the theory of random processes with special emphasis on Gaussian processes, including isoperimetric inequalities, estimates of small deviation inequalities with respect to various norms, and the functional law of the iterated logarithm. We give a short survey and provide a bibliography concerning approximation of the random fields of growing parametric dimension and probabilistic models of gravitational systems of sticky particles including the laws of large numbers and the estimates for large deviation probabilities.