lacunary trigonometric series
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1991 ◽  
Vol 43 (5) ◽  
pp. 948-959 ◽  
Author(s):  
I. Berkes

AbstractIt 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.


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