Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ESAIM: Probability and Statistics Year : 2008

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

Abdel Berkaoui
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Mireille Bossy

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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Dates and versions

inria-00000176 , version 1 (22-07-2005)
inria-00000176 , version 2 (10-01-2006)

Identifiers

  • HAL Id : inria-00000176 , version 2

Cite

Abdel Berkaoui, Mireille Bossy, Awa Diop. Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence. ESAIM: Probability and Statistics, 2008, 12, pp.15. ⟨inria-00000176v2⟩
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