Weak and strong approximations of reflected diffusions via penalization methods

We study approximations of reflected Itô diffusions on convex subsets DD of RdRd by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable functions. In the case of Lipschitz continuous coefficients we give the rate of LpLp approximation for every p≥1p≥1. We prove that if DD is a convex polyhedron then the rate is O((lnnn)1/2), and in the general case the rate is O((lnnn)1/4).