Strong approximation of lacunary series with random gaps

Alina Bazarova, I. Berkes, Marko Raseta

Research output: Contribution to journalArticle

Abstract

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
DOIs
Publication statusAccepted/In press - May 26 2017

Fingerprint

Lacunary Series
Strong Approximation
Sum formula
Random Sequence
Periodic Functions
Smooth function
Asymptotic Behavior
Zero

Keywords

  • Lacunary series
  • Random indices
  • Wiener approximation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Strong approximation of lacunary series with random gaps. / Bazarova, Alina; Berkes, I.; Raseta, Marko.

In: Monatshefte fur Mathematik, 26.05.2017, p. 1-14.

Research output: Contribution to journalArticle

@article{c0b1b9aa2c484cd6adbd0ea44f5eb60a,
title = "Strong approximation of lacunary series with random gaps",
abstract = "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.",
keywords = "Lacunary series, Random indices, Wiener approximation",
author = "Alina Bazarova and I. Berkes and Marko Raseta",
year = "2017",
month = "5",
day = "26",
doi = "10.1007/s00605-017-1059-5",
language = "English",
pages = "1--14",
journal = "Monatshefte fur Mathematik",
issn = "0026-9255",
publisher = "Springer Wien",

}

TY - JOUR

T1 - Strong approximation of lacunary series with random gaps

AU - Bazarova, Alina

AU - Berkes, I.

AU - Raseta, Marko

PY - 2017/5/26

Y1 - 2017/5/26

N2 - 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.

AB - 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.

KW - Lacunary series

KW - Random indices

KW - Wiener approximation

UR - http://www.scopus.com/inward/record.url?scp=85019720164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019720164&partnerID=8YFLogxK

U2 - 10.1007/s00605-017-1059-5

DO - 10.1007/s00605-017-1059-5

M3 - Article

SP - 1

EP - 14

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

ER -