Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables

Maria Rosaria Formica; Yuriy Vasil’ovich Kozachenko; Eugeny Ostrovsky; Leonid Sirota

doi:10.1007/s10986-020-09481-x

Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables

Maria Rosaria Formica
, Yuriy Vasil’ovich Kozachenko
, Eugeny Ostrovsky
, Leonid Sirota

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We derive exponential bounds for the tail of the distribution of normalized sums of triangular arrays of random variables, not necessarily independent, under the law of ordinary logarithm. Furthermore, we provide estimates for partial sums of triangular arrays of independent random variables belonging to suitable grand Lebesgue spaces and having heavy-tailed distributions.

Original language	English
Pages (from-to)	330-358
Number of pages	29
Journal	Lithuanian Mathematical Journal
Volume	60
Issue number	3
DOIs	https://doi.org/10.1007/s10986-020-09481-x
State	Published - 1 Jul 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

The author has been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Università degli Studi di Napoli Parthenope through the project “sostegno alla Ricerca individuale”.

Funders
GNAMPA
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Napoli Parthenope

Keywords

Cramer condition
Orlicz spaces
array of random variables
grand Lebesgue spaces
law of iterated logarithm
law of ordinary logarithm
slowly and regularly varying functions
tail function

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10.1007/s10986-020-09481-x

Cite this

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AU - Sirota, Leonid

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KW - Cramer condition

KW - Orlicz spaces

KW - array of random variables

KW - grand Lebesgue spaces

KW - law of iterated logarithm

KW - law of ordinary logarithm

KW - slowly and regularly varying functions

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Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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