A symmetrized Euler scheme for an efficient approximation of reflected diffusions

Mireille Bossy; Emmanuel Gobet; Denis Talay

doi:10.1239/jap/1091543431

A symmetrized Euler scheme for an efficient approximation of reflected diffusions

Mireille Bossy
, Emmanuel Gobet
, Denis Talay

INRIA

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	877-889
Number of pages	13
Journal	Journal of Applied Probability
Volume	41
Issue number	3
DOIs	https://doi.org/10.1239/jap/1091543431
Publication status	Published - 1 Sept 2004

Keywords

Discretization scheme
Neumann boundary condition for parabolic PDE
Reflected diffusion
Weak approximation

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10.1239/jap/1091543431

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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.",

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AU - Gobet, Emmanuel

AU - Talay, Denis

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N2 - 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.

AB - 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.

KW - Discretization scheme

KW - Neumann boundary condition for parabolic PDE

KW - Reflected diffusion

KW - Weak approximation

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DO - 10.1239/jap/1091543431

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ER -

A symmetrized Euler scheme for an efficient approximation of reflected diffusions

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Keywords

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