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

Abdel Berkaoui 1 Mireille Bossy 2, 3 Awa Diop 2, 3
3 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |x|^a, a in [1/2,1). In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
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https://hal.inria.fr/inria-00000176
Contributor : Mireille Bossy <>
Submitted on : Tuesday, January 10, 2006 - 11:01:47 AM
Last modification on : Friday, April 19, 2019 - 11:01:18 AM
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Abdel Berkaoui, Mireille Bossy, Awa Diop. Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence. ESAIM: Probability and Statistics, EDP Sciences, 2008, 12, pp.15. ⟨inria-00000176v2⟩

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