Pathwise differentiability for SDEs in a smooth domain with reflection. (English) Zbl 1231.60050
Summary: We study a Skorohod SDE in a smooth domain with normal reflection at the boundary; in particular, we prove that the solution is pathwise differentiable with respect to the deterministic starting point. The resulting derivatives evolve according to an ordinary differential equation, when the process is in the interior of the domain, and they are projected to the tangent space, when the process hits the boundary.
MSC:
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
60J55 | Local time and additive functionals |
60G17 | Sample path properties |