Pathwise differentiability for SDEs in a smooth domain with reflection

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In this paper 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.
Original languageEnglish
Article number28
Pages (from-to)845-879
Number of pages35
JournalElectronic Journal of Probability
Publication statusAccepted/In press - 1 Apr 2011


  • Stochastic differential equation with reflection
  • Normal reflection
  • Local time


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