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Nongaussian Limit Distributions of Lacunary Trigonometric Series

Published online by Cambridge University Press:  20 November 2018

I. Berkes
I. Berkes*
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, H-1053 Budapest, Reáltanoda u. 13-15, Hungary
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Abstract

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It is a well known fact that for rapidly increasing nkthe sequence , behaves like a sequence of independent random variables; in particular has a limiting Gaussian distribution as N → ∞. Under a certain critical speed this result breaks down and becomes strongly dependent. The purpose of this paper is to investigate the asymptotic behavior of normed sums in the strongly dependent domain; specifically, we construct a large class of nongaussian limit distributions of such sums.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 948 - 959
Copyright
Copyright © Canadian Mathematical Society 1991

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