Lacunary series and stable distributions
Probability
2017-07-28 v1 Functional Analysis
Number Theory
Abstract
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence of random variables to have a subsequence whose weighted partial sums, suitably normalized, converge weakly to a stable distribution with parameter .
Cite
@article{arxiv.1707.08890,
title = {Lacunary series and stable distributions},
author = {I. Berkes and R. Tichy},
journal= {arXiv preprint arXiv:1707.08890},
year = {2017}
}