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Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence

Published online by Cambridge University Press:  13 November 2007

Abdel Berkaoui ,
Mireille Bossy  and
Awa Diop
Abdel Berkaoui
Affiliation:
Dept of Statistics, University of Warwick, Gibbet Hill road, Coventry CV4 7AL, UK; berkaoui@stats.warwick.ac.uk
Mireille Bossy
Affiliation:
OMEGA project, INRIA Sophia Antipolis, 2004 route des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France; mireille.bossy@sophia.inria.fr; ADiop@bbspinc.com
Awa Diop
Affiliation:
OMEGA project, INRIA Sophia Antipolis, 2004 route des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France; mireille.bossy@sophia.inria.fr; ADiop@bbspinc.com
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Abstract

We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form|x|α , α ∈ [1/2,1). In that case, we study the rate of convergence of asymmetrized version of the Euler scheme. This symmetrized version iseasy to simulate on a computer. We prove its strong convergence and obtain the same rate ofconvergence as when the coefficients are Lipschitz.

Keywords

Discretization schemestrong convergenceCIR process.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 1 - 11
Copyright
© EDP Sciences, SMAI, 2008

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