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A sharp Abelian theorem for the Laplace transform

Abstract : 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.
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Contributor : Michel Broniatowski <>
Submitted on : Thursday, March 20, 2014 - 12:23:21 PM
Last modification on : Thursday, March 21, 2019 - 2:19:36 PM
Document(s) archivé(s) le : Friday, June 20, 2014 - 11:15:44 AM


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  • HAL Id : hal-00865680, version 4
  • ARXIV : 1309.6267


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⟩



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