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 Electronic Journal of Probability > Vol. 1 (1996) > Paper 11 open journal systems 


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.


Full text: PDF

Pages: 1-29

Published on: August 16, 1996
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Electronic Journal of Probability. ISSN: 1083-6489