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Acta Mathematica Hungarica

, Volume 144, Issue 1, pp 150–161 | Cite as

On Lacunary Series with Random Gaps

  • M. RasetaEmail author
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.

Key words and phrases

law of the iterated logarithm lacunary series random index 

Mathematics Subject Classification

primary 60F17 42A55 42A61 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Institute of StatisticsGraz University of TechnologyGrazAustria

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