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Zbl 1183.65004
Berkaoui, Abdel; Bossy, Mireille; Diop, Awa
Euler scheme for SDEs with non-lipschitz diffusion coefficient: Strong convergence. (English)
[J] ESAIM, Probab. Stat. 12, 1-11 (2008). ISSN 1292-8100; ISSN 1262-3318/e

Summary: We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form $\vert x\vert^\alpha $, $\alpha \in [1/2,1)$. 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.

MSC 2000:: *65C30 Stochastic differential and integral equations
60H35 Computational methods for stochastic equations
60H10 Stochastic ordinary differential equations
60H35 Computational methods for stochastic equations
34F05 ODE with randomness
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE

Keywords: discretization scheme; strong convergence; stochastic differential equations; Euler scheme

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