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Small Deviation Probabilities for Sums of Independent Positive Random Variables

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Abstract

We study the asymptotic behavior at zero of distributions and densities of a sum of several independent positive random variables under certain assumptions on the decay rate of their distributions at zero. We consider cases where the distributions (densities) of summable random variables are regularly or slowly varying at zero or can decrease at zero at an arbitrary rate.

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ACKNOWLEDGMENTS

The author is grateful to the referees for their informal attitude to the paper.

Funding

This work was supported by the Russian Foundation for Basic Research (grant no. 19-01-00356).

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Authors and Affiliations

  1. St. Petersburg State Chemical Pharmaceutical University, 197022, St. Petersburg, Russia

    L. V. Rozovsky

Authors
  1. L. V. Rozovsky
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Correspondence to L. V. Rozovsky.

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Translated by I. Tselishcheva

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Rozovsky, L.V. Small Deviation Probabilities for Sums of Independent Positive Random Variables. Vestnik St.Petersb. Univ.Math. 53, 295–307 (2020). https://doi.org/10.1134/S1063454120030103

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  • DOI: https://doi.org/10.1134/S1063454120030103

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