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The generator of the transition semigroup corresponding to a stochastic variational inequality. (English) Zbl 1155.60034
It is proved that the generator of the transition semigroup associated to a stochastic differential equation on a convex set with reflecting boundary is the realization of a second order elliptic operator on this set with zero oblique derivative boundary conditions. This result is applied to the invariant measure and the well posed property for parabolic problems with oblique boundary derivative conditions.

MSC:
60J60 Diffusion processes
58E35 Variational inequalities (global problems) in infinite-dimensional spaces
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