A Sharp Abelian Theorem for the Laplace Transform

Maëva Biret (), Michel Broniatowski () and Zansheng Cao ()
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Maëva Biret: Snecma Villaroche
Michel Broniatowski: Université Pierre et Marie Curie, LSTA
Zansheng Cao: Université de Strasbourg, IRMA

A chapter in Mathematical Statistics and Limit Theorems, 2015, pp 67-92 from Springer

Abstract: Abstract This paper states asymptotic equivalents for the moments of the Esscher transform of a distribution on $$\mathbb {R}$$ R with smooth density in the upper tail. As a by-product it 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.

Keywords: Tail Approximation; Gaussian Behavior; Assumed Regularity Conditions; Tilted Density; Abelian-type Theorem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12442-1_5

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DOI: 10.1007/978-3-319-12442-1_5

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