Uniqueness for the Skorokhod Equation with Normal Reflection in Lipschitz Domains
Richard F. Bass, University of Washington
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.
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