Characteristic Functions and Compactness of Distributions of Sums of Independent Random Variables

Resumo

The sequences of distributions of centered sums of independent random variables are considered within the framework of the series scheme, without assuming the classical conditions for uniform asymptotic smallness and uniform limit constancy. Necessary and sufficient conditions are obtained for relative and stochastic compactness of such sequences in terms of the characteristic functions of summable random variables and with using their τ-centers.