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May, 1985 Reflected Diffusion Processes with Jumps
Jose-Luis Menaldi, Maurice Robin
Ann. Probab. 13(2): 319-341 (May, 1985). DOI: 10.1214/aop/1176992994


A stochastic differential equation of Wiener-Poisson type is considered in a $d$-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion.


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Jose-Luis Menaldi. Maurice Robin. "Reflected Diffusion Processes with Jumps." Ann. Probab. 13 (2) 319 - 341, May, 1985.


Published: May, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0565.60065
MathSciNet: MR781408
Digital Object Identifier: 10.1214/aop/1176992994

Primary: 60J60
Secondary: 35J70

Keywords: Diffusion processes , variational inequalities

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • May, 1985
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