Applebaum, D. (2006) Brownian motion and Levy processes on locally compact groups. Methods of Functional Analysis and Topology, 12 (2). pp. 101-112.
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.
|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.|
|Institution:||The University of Sheffield|
|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:||16 Nov 2015 11:48|
|Publisher:||Institute of Mathematics, National Academy of Sciences of Ukraine|