Lacunary series and stable distributions

István Berkes; Robert Tichy

doi:10.1007/978-3-319-12442-1_2

Lacunary series and stable distributions

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence (Xn) of random variables to have a subsequence (Xnk) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter 0 < α < 2.

Original language	English
Title of host publication	Mathematical Statistics and Limit Theorems
Subtitle of host publication	Festschrift in Honour of Paul Deheuvels
Place of Publication	New York
Publisher	Springer
Pages	7-19
DOIs	https://doi.org/10.1007/978-3-319-12442-1_2
Publication status	Published - 2015
Event	60. Anniversary Conference of Paul Deheuvels - Paris, France Duration: 19 Jun 2014 → 21 Jun 2014

Conference

Conference	60. Anniversary Conference of Paul Deheuvels
Country/Territory	France
City	Paris
Period	19/06/14 → 21/06/14

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

Access to Document

10.1007/978-3-319-12442-1_2

lacunary_series_and_stable_distributionsAccepted author manuscript, 84.3 KBLicence: CC BY 4.0

Cite this

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title = "Lacunary series and stable distributions",

abstract = "By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence (Xn) of random variables to have a subsequence (Xnk) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter 0 < α < 2.",

author = "Istv{\'a}n Berkes and Robert Tichy",

year = "2015",

doi = "10.1007/978-3-319-12442-1\_2",

language = "English",

pages = "7--19",

booktitle = "Mathematical Statistics and Limit Theorems",

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AU - Berkes, István

AU - Tichy, Robert

PY - 2015

Y1 - 2015

N2 - By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence (Xn) of random variables to have a subsequence (Xnk) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter 0 < α < 2.

AB - By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence (Xn) of random variables to have a subsequence (Xnk) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter 0 < α < 2.

U2 - 10.1007/978-3-319-12442-1_2

DO - 10.1007/978-3-319-12442-1_2

M3 - Conference paper

SP - 7

EP - 19

BT - Mathematical Statistics and Limit Theorems

PB - Springer

CY - New York

T2 - 60. Anniversary Conference of Paul Deheuvels

Y2 - 19 June 2014 through 21 June 2014

ER -

Lacunary series and stable distributions

Abstract

Conference

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Fingerprint

Cite this