On some versions of non-classical central limit theorem.

Abstract

The condition of the smallness of the uniform limit of terms is the basis of the classical limit theorems for sums of independent random variables. Do not use the condition of uniform infinitesimal terms limit theorems are usually called non-classical. It is well known also that the schemes summation of independent variables is often more convenient to deal with the very distributions and formulate the conditions in limit theorems based directly on the allocation constraints. However, in our time, the characteristic functions of the device firmly entrenched in probability theory as the basis of one of themselves powerful techniques used in it. However, the proof of the convergence of series of independent random variables in terms of the characteristic functions are devoted to sravntielno little work. This work is devoted to the proof of some non-classical limit theorems formulated in terms of characteristic functions, conditions.