# On the uniqueness problem for continuous convolution semigroups of probability measures on simply connected nilpotent Lie groups

### Details

Serval ID

serval:BIB_8432

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

On the uniqueness problem for continuous convolution semigroups of probability measures on simply connected nilpotent Lie groups

Journal

Publicationes Mathematicae Debrecen

ISSN

0033-3883

Publication state

Published

Issued date

1998

Peer-reviewed

Oui

Volume

53

Number

3-4

Pages

415-422

Language

english

Abstract

Let G be a simply connected nilpotent Lie group and assume {mu(t)((i))}(t greater than or equal to 0) (i = 1, 2) are Poisson semigroups of probability measures on G with boundedly sup(1) (2)1 then P(1) (2) for all t > 0. ported Levy measures. We prove that if mu(1)((1)) = mu(1)((2)), then mu(t)((1)) = mu(t)((2)) for all t greater than or equal to 0. As a consequence, e.g. a convergent triangular system of rowwise i.i.d. probability measures on G which are concentrated on a fixed circular annulus automatically converges functionally.

Keywords

Poisson semigroups, Embedding problem, Nilpotent Lie groups

OAI-PMH

Web of science

Create date

19/11/2007 10:37

Last modification date

03/03/2018 17:54