## The Annals of Probability

### Reflected Diffusion Processes with Jumps

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 13, Number 2 (1985), 319-341.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992994

Digital Object Identifier
doi:10.1214/aop/1176992994

Mathematical Reviews number (MathSciNet)
MR781408

Zentralblatt MATH identifier
0565.60065

JSTOR