DUALITY AND MULTIPLICATIVE STOCHASTIC-PROCESSES ON QUANTUM GROUPS

An analogue of McKean's stochastic product integral is introduced and used to define stochastic processes with independent increments on qua ntum groups. The explicit form of the dual pairing (q-analogue of the exponential map) is calculated for a large class of quantum groups. Th e constructed processes are shown to satisfy generalized Feynman-Kac t ype formulas, and polynomial solutions of associated evolution equatio ns are introduced in the form of Appell systems. Explicit calculations for Gauss and Poisson processes complete the presentation.