LAUSR

We approximate of solutions of stochastic differential equations driven by Brownian motion in a smooth domain and obliquely (not necessarily normally) reflected at the boundary. This approximation is done by replacing reflection term with a penalty function: an additional drift term at the boundary pointing inside the domain. Most literature on this topic is devoted to the half-line (one-dimensional case) or to the normal reflection. We propose a large class of penalty functions and show very general weak convergence results. We perform numerical simulations to assess approximation quality for various penalty functions.