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Uniqueness for the Skorokhod Equation with Normal Reflection in Lipschitz Domains


 
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1. Title Title of document Uniqueness for the Skorokhod Equation with Normal Reflection in Lipschitz Domains
 
2. Creator Author's name, affiliation, country Richard F. Bass; University of Washington
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Lipschitz domains, Neumann problem, reflecting Brownian motion, mixed boundary problem, Skorokhod equation, weak uniqueness, uniqueness in law, submartingale problem
 
3. Subject Subject classification Primary 60J60, Secondary 60J50
 
4. Description 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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7. Date (YYYY-MM-DD) 1996-08-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/11
 
10. Identifier Digital Object Identifier 10.1214/EJP.v1-11
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 1
 
12. Language English=en en
 
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