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

Free access article

Issue		ESAIM: PS Volume 5, 2001


Page(s)		261 - 297
DOI		10.1051/ps:2001112

DOI: 10.1051/ps:2001112

ESAIM: P&S, December 2001, Vol. 5, pp. 261-297

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

Emmanuel Gobet

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

(Received September 3, 2001. Revised December 10, 2001)

Abstract
This paper is concerned with the problem of simulation of $(X_t)_{0\leq t\leq T}$ , 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.

AMS Subject: 35K20, 60-08, 60J60, 65Cxx

Key words: Killed diffusion, reflected diffusion, discretization schemes, rates of convergence, weak approximation, boundary value problems for parabolic PDE.

© EDP Sciences, SMAI 2001

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.