Probabilistic proofs of large deviation results for sums of semiexponential random variables and explicit rate function at the transition

2020/07/16 by Brosset, Fabien, Klein, Thierry, Lagnoux, Agnès +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.08164

Abstract

Asymptotics deviation probabilities of the sum S n = X 1 + × × × + X n of independent and identically distributed real-valued random variables have been extensively investigated, in particular when X 1 is not exponentially integrable. For instance, A.V. Nagaev formulated exact asymptotics results for P(S n > x n) when x n > n 1/2 (see, [13, 14]). In this paper, we derive rough asymptotics results (at logarithmic scale) with shorter proofs relying on classical tools of large deviation theory and expliciting the rate function at the transition.

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