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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 887-892 (août 2008)
Doi : 10.1016/j.crma.2007.10.038
Received : 17 November 2006 ;  accepted : 22 October 2007
Uniqueness of embedding of Gaussian probability measures into a continuous convolution semigroup on simply connected nilpotent Lie groups
Unicité du plongement de mesures de probabilité gaussiennes dans un semigroupe de convolution continu sur des groupes de Lie nilpotents et simplement connexes
 

Daniel Neuenschwander a, b, c
a Université de Lausanne, École des hautes études commerciales, Institut de sciences actuarielles, CH-1015 Lausanne, Switzerland 
b Universität Bern, Institut für mathematische Statistik und Versicherungslehre, CH-3012 Bern, Switzerland 
c Université de Lyon, Université Claude Bernard Lyon 1, Institut de Science Financière et dʼAssurances, 50, Avenue Tony Garnier, F-69007 Lyon, France 

Abstract

Let   ( ) be continuous convolution semigroups on a simply connected nilpotent Lie group G . Suppose that   and that   is a Gaussian semigroup (in the sense that its generating distribution just consists of a primitive distribution and a second order differential operator). Then   for all  . To cite this article: D. Neuenschwander, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

Soient   ( ) des semigroupes de convolution continus sur un groupe de Lie G nilpotent et simplement connexe. Si   et si   est un semigroupe gaussien (au sens que sa distribution génératrice ne consiste que dʼune distribution primitive et dʼun opérateur différentiel de second ordre), alors   pour tout  . Pour citer cet article : D. Neuenschwander, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.


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