Efficient schemes for the weak approximation of reflected diffusions

In this paper, we present two new discretization schemes for reflected stochastic diSerential equations: their constructions are aimed to achieve the order l for the weak convergence, under some conditions, improving the classical order 1/2 obtained with the projected Euler scheme (see Constantini et al. [4]). We discuss the approximation of functionals of the reflected SDE, when the time interval is finite or infinite (i.e. stationary problem).