On trigonometric sums with random frequencies

Bazarova, A. and Berkes, István and Raseta, M. (2018) On trigonometric sums with random frequencies. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 55 (1). pp. 141-152. ISSN 0081-6906

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Abstract

We prove that if Ik are disjoint blocks of positive integers and nk are independent random variables on some probability space (Ω, F, P) such that nk is uniformly distributed on Ik, then N N−1/2 (sin 2πnkx − E(sin 2πnkx)) k=1 has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1), B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when nk have continuous uniform distribution on disjoint intervals Ik on the positive axis.

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