Large Deviation Probabilities for Sums of Random Variables with Heavy or Subexponential Tails

2022/11/29 by Cline, Daren B. H., Hsing, Tailen · 1 citation
#60F10 #60G50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2211.16340

Abstract

Let S_n be the sum of independent random variables with distribution F. Under the assumption that -log(1-F(x)) is slowly varying, conditions for lim_n→∞sup_{s≥ tn}|P[S_ngt;s]\over n(1-F(s))-1| =0 are given. These conditions extend and strengthen a series of previous results. Additionally, a connection with subexponential distributions is demonstrated. That is, F is subexponential if and only if the condition above holds for some t_n and lim_t→∞1-F(t+x)\over 1-F(t) = 1 \quadfor each real x.

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