A sharp Abelian theorem for the Laplace transform

Abstract

This paper states asymptotic equivalents for the three first moments of the Eescher 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.

To appear in M. Hallin, D. Mason, D. Pfeifer, and J. Steinebach Eds, Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels. Springer, 20 pages