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Brownian motion and Levy processes on locally compact groups

By D. Applebaum


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

Publisher: Institute of Mathematics, National Academy of Sciences of Ukraine
Year: 2006
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