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L\'evy Processes on Uq(g)U_q(g) as Infinitely Divisible Representations

Abstract

L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras Uq(g)U_q(g), where gg is a simple Lie algebra. Then we show how the processes themselves can be reconstructed from their generators and study several classical stochastic processes that can be associated to these processes.Comment: 13 pages, LATEX file, ASI-TPA/13/99 (TU Clausthal); 6/99 (Preprint-Reihe Mathmatik, Univ. Greifswald)

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