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.

Full Text

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},
  MRNUMBER = {MR2238032},
       URL = {http://mfat.imath.kiev.ua/article/?id=328},
}