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Uniqueness for the Skorokhod equation with normal reflection in Lipschitz domains. (English) Zbl 0888.60067
Summary: The authors 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 $$\mathbb R^d$$, $$\nu$$ 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 $$D$$. They show that in Lipschitz domains the solution to the Skorokhod equation is unique in law.

MSC:
 60J60 Diffusion processes 60J50 Boundary theory for Markov processes
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