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.
"On the existence of a time inhomogeneous skew Brownian motion and some related laws." Electron. J. Probab. 17 1 - 27, 2012. https://doi.org/10.1214/EJP.v17-1858