# D. Applebaum

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Articles: 1

### Brownian motion and Lévy processes in locally compact groups

David Applebaum

Methods Funct. Anal. Topology 12 (2006), no. 2, 101-112

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.