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arXiv · 1707.08890

Lacunary series and stable distributions

I. Berkes·R. Tichy
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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 $(X_n)$ of random variables to have a subsequence $(X_{n_k})$ whose weighted partial sums, suitably normalized, converge weakly to a stable distribution with parameter $0<\alpha<2$.

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I. Berkes, R. Tichy. 2017-07-26. Lacunary series and stable distributions. https://arxiv.org/abs/1707.08890

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