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

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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
Author(s)
Neuenschwander D.
ISSN
0026-9255
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
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