A central limit theorem for Bessel and Dunkl processes with drift

Abstract: For some discrete parameters, multivariate (Dunkl-)Bessel processes on Weyl chambers $C$ are projections of Brownian motions on Euclidean spaces $V$; the most prominent examples are Dyson Brownian motions. More generally, the projections of Brownian motions on $V$ with drift are Bessel processes with drifts on $C$, where again the associated transition densities can be described in terms of multivariate Bessel functions. Moreover, Dunkl processes with drift can be defined in an analogous way. In this paper we prove central limit theorems for these Bessel and Dunkl processes with drift for regular drift vectors, and arbitrary root systems and multiplicities. These results improve recent results of the author.