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Zbl 1067.60036
Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing
Uniqueness for reflecting Brownian motion in Lip domains. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 41, No. 2, 197-235 (2005). ISSN 0246-0203

There is a considerable literature on the construction of reflecting Brownian motion in more or less smooth domains, with either oblique or normal reflection. The main result of the paper is a proof of strong existence and pathwise uniqueness of the Skorokhod equation in a planar Lipschitz domain whose Lipschitz constant is strictly less than one: what is normal reflection on the boundary must be carefully explicated. The authors also give a counterexample showing that there exists a Lipschitz domain in the three-dimensional space whose Lipschitz constant is strictly greater than one where weak uniqueness fails for the Skorokhod equation: here some conditions on the local times are not required any longer.
[Dominique Lepingle (Orléans)]

MSC 2000:: *60H10 Stochastic ordinary differential equations
60J65 Brownian motion

Keywords: Skorokhod equation; local time; Lipschitz domain; weak uniqueness; strong existence; Pathwise uniqueness

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