Coalescence of skew Brownian motions

Abstract

The purpose of this short note is to prove almost sure coalescence of two skew Brownian motions starting from different initial points, assuming that they are driven by the same Brownian motion. The result is very simple but we would like to record it in print as it has already become the foundation of a research project of Burdzy and Chen (1999). Our theorem is a by-product of an investigation of variably skewed Brownian motion, see Barlow et al. (1999). We use exccursion theory in a manner similar to that in a paper on "perturbed Brownian motion" by Perman and Werner (1997).