Open Access

# Brownian motion and Lévy processes in locally compact groups

### Abstract

It is shown that every L\'{e}vy 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\'{e}vy process on $G$ is of pure jump type, when $G$ is totally disconnected.

### Article Information

 Title Brownian motion and Lévy processes in locally compact groups Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 2, 101-112 MathSciNet MR2238032 Copyright The Author(s) 2006 (CC BY-SA)

### Authors Information

David Applebaum
Probability and Statistics Department, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, England, S3 7RH

### Citation Example

David Applebaum, Brownian motion and Lévy processes in locally compact groups, Methods Funct. Anal. Topology 12 (2006), no. 2, 101-112.

### BibTex

@article {MFAT328,
AUTHOR = {Applebaum, David},
TITLE = {Brownian motion and Lévy processes in locally compact groups},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {2},
PAGES = {101-112},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=328},
}