  In this paper, we consider two skew Brownian motions, driven by the same
Brownian motion, with different starting points and different skewness
coefficients. We show that we can describe the evolution of the distance
between the two processes with a stochastic differential equation. This S.D.E.
possesses a jump component driven by the excursion process of one of the two
skew Brownian motions. Using this representation, we show that the local time
of two skew Brownian motions at their first hitting time is distributed as a
simple function of a Beta random variable. This extends a result by Burdzy and
Chen (2001), where the law of coalescence of two skew Brownian motions with the
same skewness coefficient is computed.
