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

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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.

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Authors and Affiliations

  1. Parthenope University of Naples, via Generale Parisi 13, Palazzo Pacanowsky, 80132, Napoli, Italy

    Maria Rosaria Formica

  2. Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yuriy Vasil’ovich Kozachenko

  3. Department of Mathematics and Statistics, Bar-Ilan University, 52900, Ramat Gan, Israel

    Eugeny Ostrovsky & Leonid Sirota

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  1. Maria Rosaria Formica
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  2. Yuriy Vasil’ovich Kozachenko
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  3. Eugeny Ostrovsky
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  4. Leonid Sirota
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Correspondence to Maria Rosaria Formica.

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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”.

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Formica, M.R., Vasil’ovich Kozachenko, Y., Ostrovsky, E. et al. Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables. Lith Math J 60, 330–358 (2020). https://doi.org/10.1007/s10986-020-09481-x

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  • DOI: https://doi.org/10.1007/s10986-020-09481-x

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