A sharp Abelian theorem for the Laplace transform

Maeva Biret (1) , Michel Broniatowski (1) , Zhansheng Cao (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

This paper states asymptotic equivalents for the moments of the Esscher transform of a distribution on R with smooth density in the upper tail. As a by product if provides a tail approximation for its moment generating function, and shows that the Esscher transforms have a Gaussian behavior for large values of the parameter.

Mots clés: Abelian theorem; Laplace transform; Esscher transform; tilted distribution

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Analyse classique [math.CA]

Maeva Biret, Michel Broniatowski, Zhansheng Cao. A sharp Abelian theorem for the Laplace transform. M Hallin, D M Mason, D. Pfeiffer, J Steinebach. Mathematical statistics and limit theorems, 67–92, Springer, Cham, Springer, Cham, pp.67-92, 2015. ⟨hal-00865680v4⟩