2020/10/19 by Thierry Klein, Klein, Thierry, Agnès Lagnoux +2
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2010.09276
openalex publication_date 2020/10/19 · openalex created_date 2022/02/24 · openalex updated_date 2026/07/28
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 1 has a semiexponential distribution (see, [16, 17]). In the same setting, the authors of [4] derived deviation results at logarithmic scale with shorter proofs relying on classical tools of large deviation theory and expliciting the rate function at the transition. In this paper, we exhibit the same asymptotic behaviour for triangular arrays of semiexponentially distributed random variables, no more supposed absolutely continuous.