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

Gobet, Emmanuel

ESAIM: Probability and Statistics, Tome 5 (2001), pp. 261-297.

This paper is concerned with the problem of simulation of ${\left(X_t\right)}_{0\le t\le T}$, 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 $\partial D$ 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.

Classification : 35K20, 60-08, 60J60, 65Cxx
Mots clés : killed diffusion, reflected diffusion, discretization schemes, rates of convergence, weak approximation, boundary value problems for parabolic PDE

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