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