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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.

60J60 Diffusion processes
60J50 Boundary theory for Markov processes
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