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 |
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Pages (from-to) | 330-358 |
Number of pages | 29 |
Journal | Lithuanian Mathematical Journal |
Volume | 60 |
Issue number | 3 |
DOIs | |
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 | Funder number |
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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