EVOLUTION-EQUATIONS AND LEVY PROCESSES ON QUANTUM GROUPS

Evolution equations like the heat or diffusion equation or the Schrodi nger equation can be associated with stochastic processes. In this pap er we study the relation between equations of the form partial derivat ive(t)u = Lu and Levy processes (i.e. quantum stochastic processes wit h independent and stationary increments) on quantum groups and braided groups. Solutions of such equations are calculated as Appell systems. Wigner distributions of these processes are defined and it is proven that they satisfy a Fokker-Planck equation.