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January, 1993 SDEs with Oblique Reflection on Nonsmooth Domains
Paul Dupuis, Hitoshi Ishii
Ann. Probab. 21(1): 554-580 (January, 1993). DOI: 10.1214/aop/1176989415


In this paper we consider stochastic differential equations with reflecting boundary conditions for domains that might have corners and for which the allowed directions of reflection at a point on the boundary of the domain are possibly oblique. The main results are strong existence and uniqueness for solutions of such equations. A key ingredient is a family of relatively regular functions appropriate to the given domain and directions of reflection. Two cases are treated in the paper. In the first case the direction of reflection is single valued and varies smoothly, and the main new feature is that the boundary of the domain may be nonsmooth. In the second case the domain is taken to be the intersection of a finite number of domains with relatively smooth boundary, and at the resulting corner points more than one oblique direction is allowed.


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Paul Dupuis. Hitoshi Ishii. "SDEs with Oblique Reflection on Nonsmooth Domains." Ann. Probab. 21 (1) 554 - 580, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0787.60099
MathSciNet: MR1207237
Digital Object Identifier: 10.1214/aop/1176989415

Primary: 60J60
Secondary: 60J50

Keywords: nonsmooth domains , Reflected diffusions , Skorokhod problem , Stochastic differential equations with reflection

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • January, 1993
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