Year: 2025
Type: preprint
Abstract: For certain discrete multiplicity parameters $k\ge0$, multivariate (Dunkl-)Bessel processes on Weyl chambers $C$ associated with root systems appear as projections of Brownian motions without drift on Euclidean spaces $V$, and the associated transition densities can be described in terms of multivariate Bessel functions; the most prominent examples are Dyson Brownian motions. The projections of Brownian motions on $V$ with drifts are also Feller diffusions on $C$, and their transition densities and their generators can be again described via these Bessel functions. These processes are called Bessel processes with drifts. In this paper we construct these Bessel processes processes with drift for arbitrary root systems and parameters $k\ge 0$. Moreover, this construction works also for Dunkl processes. We study some features of these processes with drift like their radial parts, a Girsanov theorem, moments and associated martingales, strong laws of large numbers, and central limit theorems.
Source: arXiv (Cornell University)
Author: Voit, Michael
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417296451
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