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

Published online by Cambridge University Press:  15 August 2002

Emmanuel Gobet
Emmanuel Gobet*
Affiliation:
École Polytechnique, Centre de Mathématiques Appliquées, 91128 Palaiseau Cedex, France; emmanuel.gobet@polytechnique.fr.
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Abstract

This paper is concerned with the problem of simulation of (Xt)0≤t≤T , thesolution of a stochastic differential equation constrained by some boundary conditions in a smooth domainD: namely, we consider the case where the boundary ∂D is killing, or where it is instantaneouslyreflecting 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 orderN -1 under some conditions. The construction of these schemes is based on a natural principle of localapproximation of the domain into a half space, for which efficient simulations are available.

Keywords

Killed diffusionreflected diffusiondiscretization schemesrates of convergenceweakapproximationboundary value problems for parabolic PDE.

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 5 , 2001 , pp. 261 - 297
Copyright
© EDP Sciences, SMAI, 2001

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