Lévy Processes on $U_q(g)$ as Infinitely Divisible Representations

Details Lévy Processes on $U_q(g)$ as Infinitely Divisible Representations Lévy Processes on $U_q(g)$ as Infinitely Divisible Representations

1999-07-02

arxiv.org/abs/math/9907016v1

Contemp. Math. 261 (2000) 181-192

Mathematics

Probability

13 pages, LATEX file, ASI-TPA/13/99 (TU Clausthal); 6/99 (Preprint-Reihe Mathmatik, Univ. Greifswald);

Scientific paper

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 $U_q(g)$, where $g$ 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.

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