TY - JOUR

T1 - Toward the History of the Saint Petersburg School of Probability and Statistics. I. Limit Theorems for Sums of Independent Random Variables

AU - Lifshits, M.A.

AU - Nikitin, Ya. Yu.

AU - Petrov, V.V.

AU - Zaitsev, A. Yu.

AU - Zinger, A. A.

N1 - Lifshits, M.A., Nikitin, Y.Y., Petrov, V.V. et al. Toward the History of the Saint Petersburg School of Probability and Statistics. I. Limit Theorems for Sums of Independent Random Variables. Vestnik St.Petersb. Univ.Math. 51, 144–163 (2018). https://doi.org/10.3103/S1063454118020115

PY - 2018/6/15

Y1 - 2018/6/15

N2 - 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.

AB - 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.

KW - sums of independent random variables, central limit theorem, law of large numbers, law of the iterated logarithm, infinitely divisible distributions, concentration functions, Littlewood–Offord problem, empirical measure, almost sure limit theorem

KW - almost sure limit theorem

KW - central limit theorem

KW - concentration functions

KW - empirical measure

KW - infinitely divisible distributions

KW - law of large numbers

KW - law of the iterated logarithm

KW - Littlewood–Offord problem

KW - sums of independent random variables

UR - http://www.scopus.com/inward/record.url?scp=85048653129&partnerID=8YFLogxK

U2 - 10.3103/S1063454118020115

DO - 10.3103/S1063454118020115

M3 - Article

VL - 51

SP - 144

EP - 163

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -