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arXiv · 1509.08138

On the strong approximations of partial sums of f(nkx)

Marko Raseta
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Abstract

We prove a strong invariance principle for the sums PN k=1 f(nkx), where f is a smooth periodic function on R and (nk)k?1 is an increasing random sequence. Our results show that in contrast to the classical Salem-Zygmund theory, the asymptotic properties of lacunary series with random gaps can be described very precisely without any assumption on the size of the gaps.

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Marko Raseta. 2015-09-27. On the strong approximations of partial sums of f(nkx). https://arxiv.org/abs/1509.08138

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