This is the second paper in a series of reviews devoted to the scientific achievements of the Leningrad and St. Petersburg school of probability and mathematical statistics from 1947 to 2017. This paper is devoted to the works on limit theorems for dependent variables (in particular, Markov chains, sequences with mixing properties, and sequences admitting a martingale approximation) and to various aspects of the theory of random processes. We pay particular attention to Gaussian processes, including isoperimetric inequalities, estimates of the probabilities of small deviations in various norms, and the functional law of the iterated logarithm. We present a brief review and bibliography of the works on approximation of random fields with a parameter of growing dimension and probabilistic models of systems of sticky inelastic particles (including laws of large numbers and estimates for the probabilities of large deviations).

Translated title of the contributionОб истории Санкт-Петербургской школы теории вероятностей и математической статистики II Случайные процессы и зависимые величины
Original languageEnglish
Pages (from-to)213-236
Number of pages24
JournalVestnik St. Petersburg University: Mathematics
Issue number3
Publication statusPublished - 1 Jul 2018

Scopus subject areas

  • Mathematics(all)

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