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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.


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Article Information

TitleBrownian motion and Lévy processes in locally compact groups
SourceMethods Funct. Anal. Topology, Vol. 12 (2006), no. 2, 101-112
MathSciNet MR2238032
CopyrightThe 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 


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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},
}


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