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On Lacunary Series with Random Gaps

Acta Mathematica Hungarica volume 144, pages 150–161 (2014)Cite this article

Abstract

Abstract We prove Strassen’s law of the iterated logarithm for sums \({\sum^{N}_{k=1} f(n_kx),}\) where f is a smooth periodic function on the real line and \({(n_k)_{k \geqq 1}}\) is an increasing random sequence. Our results show that classical results of the theory of lacunary series remain valid for sequences with random gaps, even in the nonharmonic case and if the Hadamard gap condition fails.

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Authors and Affiliations

  1. Institute of Statistics, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria

    M. Raseta

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  1. M. Raseta
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Correspondence to M. Raseta.

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Research supported by FWF Projekt W1230.

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Raseta, M. On Lacunary Series with Random Gaps. Acta Math. Hungar. 144, 150–161 (2014). https://doi.org/10.1007/s10474-014-0430-4

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  • DOI: https://doi.org/10.1007/s10474-014-0430-4

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