Tauberian results for densities with gaussian tails

A. A. Balkema, C. Klüppelberg, U. Stadtmüller

Research output: Contribution to journalArticlepeer-review

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We study a class of probability densities with very thin upper tails. These densities generate exponential families which are asymptotically normal. Furthermore the class is closed under convolution. In this paper we shall be concerned with Abelian and strong Tauberian theorems for moment generating functions and Laplace transforms with respect to these densities. We obtain a duality relation between this class of densities and the associated class of moment generating functions which is closely related to the duality relation for convex functions.

Original languageEnglish
Pages (from-to)383-400
Number of pages18
JournalJournal of the London Mathematical Society
Issue number2
StatePublished - Apr 1995
Externally publishedYes


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