# Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

## Details

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It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.

State: Public

Version: Final published version

License: Not specified

It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.

Serval ID

serval:BIB_0CB0D7488F91

Type

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

Collection

Publications

Institution

Title

Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

Journal

Monatshefte für Mathematik

ISSN

0026-9255

1436-5081

1436-5081

Publication state

Published

Issued date

07/2013

Peer-reviewed

Oui

Volume

171

Number

1

Pages

91-101

Language

english

Abstract

Let {mu((i))(t)}(t >= 0) (i = 1, 2) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that mu((1))(1) = mu((2))(1). Assume furthermore that {mu((1))(t)}(t >= 0) is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then mu((1))(1) = mu((2))(1) for all t >= 0. We end up with a possible application in mathematical finance.

Keywords

Continuous convolution semigroups of probability measures, Affine group, Levy processes, Brownian motion

Web of science

Open Access

Yes

Create date

20/07/2017 11:10

Last modification date

01/10/2019 7:16