Toward the History of the Saint Petersburg School of Probability and Statistics. I. Limit Theorems for Sums of Independent Random Variables

M.A. Lifshits, Ya. Yu. Nikitin, V.V. Petrov, A. Yu. Zaitsev, A. A. Zinger

Research output

2 Citations (Scopus)

Abstract

This is the first in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg school of probability and statistics in the period from 1947 to 2017. It is devoted to limit theorems for sums of independent random variables—a traditional subject for St. Petersburg. It refers to the classical limit theorems: the law of large numbers, the central limit theorem, and the law of the iterated logarithm, as well as important relevant problems formulated in the second half of the twentieth century. The latter include the approximation of the distributions of sums of independent variables by infinitely divisible distributions, estimation of the accuracy of strong Gaussian approximation of such sums, and the limit theorems on the weak almost sure convergence of empirical measures generated by sequences of sums of independent random variables and vectors.
Translated title of the contributionК истории санкт-петербургской школы по теории вероятностей и математической статистике. I : Предельные теоремы для сумм независимых случайных величин
Original languageEnglish
Pages (from-to)144-163
Number of pages20
JournalVestnik St. Petersburg University: Mathematics
Volume51
Issue number2
DOIs
Publication statusPublished - 15 Jun 2018

Scopus subject areas

  • Mathematics(all)

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