A sharp Abelian theorem for the Laplace transform
Statistics Theory
2014-03-21 v4 Classical Analysis and ODEs
Statistics Theory
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.
Cite
@article{arxiv.1309.6267,
title = {A sharp Abelian theorem for the Laplace transform},
author = {Maeva Biret and Michel Broniatowski and Zhansheng Cao},
journal= {arXiv preprint arXiv:1309.6267},
year = {2014}
}
Comments
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