caa a22 4500 397533438 CHVBK 20180308164657.0 cr unu---uuuuu 161202e199504 xx s 000 0 eng 10.1112/jlms/51.2.383 doi (NATIONALLICENCE)oxford-10.1112/jlms/51.2.383 Tauberian Results for Densities with Gaussian Tails [Elektronische Daten] [A. A. Balkema, C. Klüppelberg, U. Stadtmüller] 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. © The London Mathematical Society Notes and Papers nationallicence Balkema A. A. University of Amsterdam FWI, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands aut Klüppelberg C. ETH-Zürich, Departement Mathematik CH-8092 Zürich, Switzerland aut Stadtmüller U. Universität Ulm Abteilung Mathematik III, Helmholtzstrasse 18, 89069 Ulm, Germany aut Journal of the London Mathematical Society Oxford University Press 51/2(1995-04), 383-400 0024-6107 51:2<383 1995 51 jlms https://doi.org/10.1112/jlms/51.2.383 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1112/jlms/51.2.383 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balkema A. A. University of Amsterdam FWI, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands aut NATIONALLICENCE 700 1- Klüppelberg C. ETH-Zürich, Departement Mathematik CH-8092 Zürich, Switzerland aut NATIONALLICENCE 700 1- Stadtmüller U. Universität Ulm Abteilung Mathematik III, Helmholtzstrasse 18, 89069 Ulm, Germany aut NATIONALLICENCE 773 0- Journal of the London Mathematical Society Oxford University Press 51/2(1995-04), 383-400 0024-6107 51:2<383 1995 51 jlms Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford