We consider the Skorokhod equation $$dX_t=dW_t+(1/2)\nu(X_t), dL_t$$ in a domain $D$, where $W_t$ is Brownian motion in $R^d$, $\nu$ is the inward pointing normal vector on the boundary of $D$, and $L_t$ is the local time on the boundary. The solution to this equation is reflecting Brownian motion in $D$. In this paper we show that in Lipschitz domains the solution to the Skorokhod equation is unique in law.
"Uniqueness for the Skorokhod Equation with Normal Reflection in Lipschitz Domains." Electron. J. Probab. 1 1 - 29, 1996. https://doi.org/10.1214/EJP.v1-11