I am studying reflected brownian motion. I have already understood the 1-D case, and I am able to reproduce the probability density functions for reflected brownain motion on arbitrary closed intervals. I think the next simple case is to study reflected brownian motion inside a disk. Is it possible to obtain, as in the 1-d case, closed formulas for the PDF of reflected brownian motion in a disk (whose boundary of reflection would be $\mathbb S^1$)?
p.d. I have searched with keywords "reflected brownian motion+disk" with no avail. I am sure, however, that relevant things to read should exist, thus any reference is welcome!