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

V. K. Dobrev , H. -D. Doebner , Uwe Franz (1) , René Schott (2, 3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 IECN - Institut Élie Cartan de Nancy

Lévy processes on bialgebras are families of infinitely divisible representations. We classify the generators of Lévy 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.

Domaines: Probabilités [math.PR]

V. K. Dobrev, H. -D. Doebner, Uwe Franz, René Schott. Lévy Processes on $U_q(g)$ as Infinitely Divisible Representations. 1999. ⟨hal-00470219⟩