Non-polar points for reflected Brownian motion

Abstract

Our main results are (i) a new construction of reflected Brownian motion X in a half-plane with non-smooth angle of oblique reflection and (ii) a theorem on existence of some "exceptional" points on the paths of the standard two-dimensional Brownian motion. The link between these two seemingly disparate results will be formed by some theorems related to the following question (iii) Which points are hit by the reflected Brownian motion X with positive probability?