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

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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https://hal.archives-ouvertes.fr/hal-02895684
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Submitted on : Wednesday, July 15, 2020 - 11:25:39 AM
Last modification on : Tuesday, October 20, 2020 - 10:32:07 AM

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  • HAL Id : hal-02895684, version 1
  • ARXIV : 2007.08164

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

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