- Autor
- Bazarova, Alina
- Berkes, István
- Raseta, Marko
- TitelStrong approximation of lacunary series with random gaps
- Datei
- DOI10.1007/s00605-017-1059-5
- Erschienen inMonatshefte für Mathematik
- Erscheinungsjahr2017
- LicenceCC BY
- ISSN1436-5081
- Download Statistik2174
- Peer ReviewNein
- AbstractWe investigate the asymptotic behavior of sums \(Σ^N_{k=1} f (n_k x)\), where f is a mean zero, smooth periodic function on \(\mathbb{R}\) and \((n_k )_{k≥1}\) is a random sequence such that the gaps \(n_{k+1} − n_k\) 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.
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