Volume 12, April 2008
|Page(s)||1 - 11|
|Published online||13 November 2007|
Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
Dept of Statistics, University of
Warwick, Gibbet Hill road, Coventry CV4 7AL, UK; firstname.lastname@example.org
2 OMEGA project, INRIA Sophia Antipolis, 2004 route des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France; email@example.com; ADiop@bbspinc.com
Revised: 30 May 2006
Revised: 8 October 2006
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.
Mathematics Subject Classification: 65C30 / 60H35 / 65C20
Key words: Discretization scheme / strong convergence / CIR process.
© EDP Sciences, SMAI, 2008
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