Convergence of series of strongly integrable random variables and applications

Fakhreddine Boukhari and Dounyazed Malti

Statistics & Probability Letters, 2018, vol. 137, issue C, 191-200

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.

Keywords: Almost sure convergence; Maximal inequalities; Subgaussian random variables; Exponential integrability; Random series (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.01.029

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