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Convergence of series of strongly integrable random variables and applications

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  • Boukhari, Fakhreddine
  • Malti, Dounyazed

Abstract

We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying these results to sequences with d-subgaussian increments, we examine the asymptotic behavior of weighted sums of subgaussian random variables in a unified setting.

Suggested Citation

  • Boukhari, Fakhreddine & Malti, Dounyazed, 2018. "Convergence of series of strongly integrable random variables and applications," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 191-200.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:191-200
    DOI: 10.1016/j.spl.2018.01.029
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    References listed on IDEAS

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    1. Amini, M. & Zarei, H. & Bozorgnia, A., 2007. "Some strong limit theorems of weighted sums for negatively dependent generalized Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1106-1110, June.
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