Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 1-11.

We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form ${|x|}^{\alpha }$, $\alpha \in \left[1/2,1\right)$. 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.

DOI : https://doi.org/10.1051/ps:2007030
Classification : 65C30,  60H35,  65C20
Mots clés : discretization scheme, strong convergence, CIR process
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author = {Berkaoui, Abdel and Bossy, Mireille and Diop, Awa},
title = {Euler scheme for {SDEs} with {non-Lipschitz} diffusion coefficient : strong convergence},
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Berkaoui, Abdel; Bossy, Mireille; Diop, Awa. Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 1-11. doi : 10.1051/ps:2007030. http://www.numdam.org/articles/10.1051/ps:2007030/

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