Brownian motion and Levy processes on locally compact groups

Applebaum, D. (2006) Brownian motion and Levy processes on locally compact groups. Methods of Functional Analysis and Topology, 12 (2). pp. 101-112.

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Abstract

It is shown that every L´evy process on a locally compact group G is determined by a sequence of one-dimensional Brownian motions and an independent Poisson random measure. As a consequence, we are able to give a very straightforward proof of sample path continuity for Brownian motion in G. We also show that every L´evy process on G is of pure jump type, when G is totally disconnected.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2006 Institute of Mathematics, National Academy of Sciences of Ukraine. This is an author produced version of a paper subsequently published in Methods of Functional Analysis and Topology. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	Locally compact group, L´evy process, topological Lie algebra, weak coordinate system, Feller semigroup, Brownian motion, Poisson random measure.
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Miss Anthea Tucker
Date Deposited:	30 Sep 2009 13:33
Last Modified:	08 Feb 2013 16:59
Published Version:	http://www.imath.kiev.ua/~mfat/html/papers/2006/2/...
Status:	Published
Publisher:	Institute of Mathematics, National Academy of Sciences of Ukraine
Refereed:	Yes
URI:	http://eprints.whiterose.ac.uk/id/eprint/9798

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