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A symmetrized Euler scheme for an efficient approximation of reflected diffusions

Part of: Probability theory and stochastic processes Parabolic equations and systems

Published online by Cambridge University Press:  14 July 2016

Mireille Bossy ,
Emmanuel Gobet  and
Denis Talay
Mireille Bossy*
Affiliation:
INRIA, Sophia-Antipolis
Emmanuel Gobet*
Affiliation:
École Polytechnique, Palaiseau
Denis Talay*
Affiliation:
INRIA, Sophia-Antipolis
*
∗ Postal address: INRIA Unité de Recherche de Sophia-Antipolis, 2004, Route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France
∗ Postal address: CMAP, École Polytechnique, 91128 Palaiseau Cedex, France. Email address: gobet@cmapx.polytechnique.fr
∗ Postal address: INRIA Unité de Recherche de Sophia-Antipolis, 2004, Route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France
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Abstract

In this article, we analyse the error induced by the Euler scheme combined with a symmetry procedure near the boundary for the simulation of diffusion processes with an oblique reflection on a smooth boundary. This procedure is easy to implement and, in addition, accurate: indeed, we prove that it yields a weak rate of convergence of order 1 with respect to the time-discretization step.

Keywords

Reflected diffusiondiscretization schemeweak approximationNeumann boundary condition for parabolic PDE

MSC classification

Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations 60-08: Computational methods (not classified at a more specific level)
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 877 - 889
Copyright
Copyright © Applied Probability Trust 2004 

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