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

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7 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 languageEnglish
Pages (from-to)330-358
Number of pages29
JournalLithuanian Mathematical Journal
Volume60
Issue number3
DOIs
StatePublished - 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”.

FundersFunder number
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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