Lacunary Series and Stable Distributions

István Berkes () and Robert Tichy ()
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István Berkes: Graz University of Technology, Institute of Statistics
Robert Tichy: Graz University of Technology, Institute of Mathematics A

A chapter in Mathematical Statistics and Limit Theorems, 2015, pp 7-19 from Springer

Abstract: 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 $$(X_n)$$ ( X n ) of random variables to have a subsequence $$(X_{n_k})$$ ( X n k ) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter $$0

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12442-1_2

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DOI: 10.1007/978-3-319-12442-1_2

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