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.
Menaldi, J.-L. and Robin, M. (1985). On some optimal stopping problems with constraint, Ann. Probab. 13 319-341. doi: 10.1214/aop/1176992994