Probabilistic proofs of large deviation results for sums of semiexponential random variables and explicit rate function at the transition - Archive ouverte HAL Access content directly
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Probabilistic proofs of large deviation results for sums of semiexponential random variables and explicit rate function at the transition

Fabien Brosset
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Thierry Klein
P Petit

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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Dates and versions

hal-02895684 , version 1 (15-07-2020)
hal-02895684 , version 2 (19-01-2021)

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Fabien Brosset, Thierry Klein, Agnès Lagnoux, P Petit. Probabilistic proofs of large deviation results for sums of semiexponential random variables and explicit rate function at the transition. 2020. ⟨hal-02895684v1⟩
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