Strong approximation of lacunary series with random gaps

Alina Bazarova; Istvan Berkes; Marko Raseta

doi:10.1007/s00605-017-1059-5

Strong approximation of lacunary series with random gaps

Alina Bazarova, Istvan Berkes^*, Marko Raseta

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Statistik (5060)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

We investigate the asymptotic behavior of sums Σ^N_k=1 f (n_kx), where f is a mean zero, smooth periodic function on IR 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.

Originalsprache	englisch
Seiten (von - bis)	393-406
Seitenumfang	14
Fachzeitschrift	Monatshefte fur Mathematik
Jahrgang	186
Ausgabenummer	3
DOIs	https://doi.org/10.1007/s00605-017-1059-5
Publikationsstatus	Veröffentlicht - 26 Mai 2017

Schlagwörter

Lacunary series
Random indices
Wiener approximation

ASJC Scopus subject areas

Allgemeine Mathematik

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10.1007/s00605-017-1059-5

strong_approximation_of_lacunary_series_with_random_gapsAkzeptiertes Autorenmanuskript, 154 KBLizenz: CC BY 4.0

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title = "Strong approximation of lacunary series with random gaps",

abstract = "We investigate the asymptotic behavior of sums ∑Nk=1f(nkx), where f is a mean zero, smooth periodic function on ℝ and (nk)k≥1 is a random sequence such that the gaps nk+1- nk 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, Lacunary series, Random indices, Wiener approximation",

author = "Alina Bazarova and Istvan Berkes and Marko Raseta",

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AU - Bazarova, Alina

AU - Berkes, Istvan

AU - Raseta, Marko

PY - 2017/5/26

Y1 - 2017/5/26

N2 - We investigate the asymptotic behavior of sums ∑Nk=1f(nkx), where f is a mean zero, smooth periodic function on ℝ and (nk)k≥1 is a random sequence such that the gaps nk+1- nk 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 ∑Nk=1f(nkx), where f is a mean zero, smooth periodic function on ℝ and (nk)k≥1 is a random sequence such that the gaps nk+1- nk 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

KW - Lacunary series

KW - Random indices

KW - Wiener approximation

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VL - 186

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EP - 406

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 3

ER -

Strong approximation of lacunary series with random gaps

Abstract

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ASJC Scopus subject areas

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