Projection scheme for stochastic differential equations with convex constraints

A numerical scheme for stochastic differential equations with convex constraints is considered. The solutions to the SDEs are constrained to the domain of convex lower semicontinuous function through a multivalued monotone drift component and a variational inequality. The projection scheme is a time discrete version of the constrained SDE. In the particular case when the constraining function is an indicator of a closed convex domain, the SDE is reflected. Previous convergence results for the projection scheme applied to reflected SDEs are recovered.