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

Abdel Berkaoui;  Mireille Bossy;  Awa Diop — 2008

ESAIM: Probability and Statistics

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 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.

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

Abdel Berkaoui;  Mireille Bossy;  Awa Diop — 2007

ESAIM: Probability and Statistics

We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |, ∈ [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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