ON NONCLASSICAL LIMIT THEOREMS FOR SUMS OF INDEPENDENT RANDOM VARIABLES

Nonclassical limit theorems, unlike classical ones, do not require satisfaction of the uniform limit smallness condition. In the nonclassical situation of summation of independent random variables, the class of limit distributions is extended maximally, and it coincides with the set of all distributions. In the paper, it is carried out the comparative analysis of the classical Kolmogorov’s model in the theory of summation of independent random variables with problems of the central limit problem in the nonclassical formulation. Also nonclassical versions of the central limit theorem are proved. In this connection, modified version of the known Stein’s method is used. This version is based on a characterized property of the normal distribution.