Probability Theory
Uniqueness of embedding of Gaussian probability measures into a continuous convolution semigroup on simply connected nilpotent Lie groups
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 887-892.

Let ${μt(i)}t⩾0$ ($i=1,2$) be continuous convolution semigroups on a simply connected nilpotent Lie group G. Suppose that $μ1(1)=μ1(2)$ and that ${μt(1)}t⩾0$ is a Gaussian semigroup (in the sense that its generating distribution just consists of a primitive distribution and a second order differential operator). Then $μt(1)=μt(2)$ for all $t⩾0$.

Soient ${μt(i)}t⩾0$ ($i=1,2$) des semigroupes de convolution continus sur un groupe de Lie G nilpotent et simplement connexe. Si $μ1(1)=μ1(2)$ et si ${μt(1)}t⩾0$ est un semigroupe gaussien (au sens que sa distribution génératrice ne consiste que d'une distribution primitive et d'un opérateur différentiel de second ordre), alors $μt(1)=μt(2)$ pour tout $t⩾0$.

Accepted:
Published online:
DOI: 10.1016/j.crma.2007.10.038
Neuenschwander, Daniel 1, 2, 3

1 Université de Lausanne, École des hautes études commerciales, Institut de sciences actuarielles, CH-1015 Lausanne, Switzerland
2 Universität Bern, Institut für mathematische Statistik und Versicherungslehre, CH-3012 Bern, Switzerland
3 Université de Lyon, Université Claude Bernard Lyon 1, Institut de Science Financière et d'Assurances, 50, Avenue Tony Garnier, F-69007 Lyon, France
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Neuenschwander, Daniel. Uniqueness of embedding of Gaussian probability measures into a continuous convolution semigroup on simply connected nilpotent Lie groups. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 887-892. doi : 10.1016/j.crma.2007.10.038. http://www.numdam.org/articles/10.1016/j.crma.2007.10.038/

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