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Uniqueness for the Skorokhod Equation with Normal Reflection in Lipschitz Domains

   
@article{EJP11,
	author = {Richard Bass},
	title = {Uniqueness for the Skorokhod Equation with Normal Reflection in Lipschitz Domains},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {1},
	year = {1996},
	keywords = {Lipschitz domains, Neumann problem, reflecting Brownian motion, mixed boundary problem, Skorokhod equation, weak uniqueness, uniqueness in law, submartingale problem},
	abstract = {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.},
	pages = {no. 11, 1-29},
	issn = {1083-6489},
	doi = {10.1214/EJP.v1-11},    
        url = {http://ejp.ejpecp.org/article/view/11}}