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Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
Abdel Berkaoui, Mireille Bossy, Awa Diop
Journal:

ESAIM: Probability and Statistics / Volume 12 / 2008

Published online by Cambridge University Press:

13 November 2007, pp. 1-11

Print publication:

2008
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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 asymmetrized version of the Euler scheme. This symmetrized version iseasy to simulate on a computer. We prove its strong convergence and obtain the same rate ofconvergence as when the coefficients are Lipschitz.