Euler schemes and half-space approximation for the simulation of diffusion in a domain

Abstract. This paper is concerned with the problem of simulation of (Xt)0tT, the solution of a sto-chastic dierential equation constrained by some boundary conditions in a smooth domain D: namely, we consider the case where the boundary @D is killing, or where it is instantaneously reflecting in an oblique direction. Given N discretization times equally spaced on the interval [0; T], we propose new discretization schemes: they are fully implementable and provide a weak error of order N−1 under some conditions. The construction of these schemes is based on a natural principle of local approximatio