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

École Polytechnique, Centre de Mathématiques Appliquées, 91128 Palaiseau Cedex, France; emmanuel.gobet@polytechnique.fr.

Received: 3 September 2001
Revised: 10 December 2001

Abstract

This paper is concerned with the problem of simulation of (X_t)_0≤t≤T, the solution of a stochastic differential 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 approximation of the domain into a half space, for which efficient simulations are available.