Convergence of series of strongly integrable random variables

TL;DR

This paper studies the convergence properties of series composed of strongly integrable and subgaussian random variables, providing conditions for convergence in exponential Orlicz norms and almost sure convergence, with applications to weighted series.

Contribution

It introduces new sufficient conditions for convergence of series of strongly integrable and subgaussian random variables, unifying their asymptotic analysis.

Findings

Established convergence criteria in exponential Orlicz norms.

Proved almost sure convergence under specified conditions.

Analyzed the asymptotic behavior of weighted subgaussian series.

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 this result to $d$-subgaussian series, we examine the asymptotic behavior of weighted series of subgaussian random variables in a unified setting. \end{abstract