On Lacunary Series with Random Gaps

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JournalActa Mathematica Hungarica
DateE-pub ahead of print - 20 Jun 2014
DatePublished (current) - Oct 2014
Issue number1
Volume144
Number of pages12
Pages (from-to)150-161
Early online date20/06/14
Original languageEnglish

Abstract

Abstract We prove Strassen's law of the iterated logarithm for sums (Formula presented.) where f is a smooth periodic function on the real line and (Formula presented.) 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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