  This article is devoted to the construction of a solution for the "skew
inhomogeneous Brownian motion" equation, which first appear in a seminal paper
by Sophie Weinryb (1983). We investigate some laws related to the constructed
process. In particular, using the description of the straddling excursion above
a deterministic time, we compute the joint law of the process, its local time
and its straddling time.

Probability