Strong approximation of lacunary series with random gaps

Alina Bazarova, I. Berkes, Marko Raseta

Research output: Contribution to journalArticle


We investigate the asymptotic behavior of sums (Formula presented.), where f is a mean zero, smooth periodic function on (Formula presented.) and (Formula presented.) is a random sequence such that the gaps (Formula presented.) are i.i.d. Our result shows that, in contrast to the classical Salem–Zygmund theory, the almost sure behavior of lacunary series with random gaps can be described very precisely without any assumption on the size of the gaps.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalMonatshefte fur Mathematik
Publication statusAccepted/In press - May 26 2017



  • Lacunary series
  • Random indices
  • Wiener approximation

ASJC Scopus subject areas

  • Mathematics(all)

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