Geodesic
Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 1-11 Cet article a éte moissonné depuis la source Numdam

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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 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 : 10.1051/ps:2007030
Classification : 65C30, 60H35, 65C20
Keywords: discretization scheme, strong convergence, CIR process 
@article{PS_2008__12__1_0,
     author = {Berkaoui, Abdel and Bossy, Mireille and Diop, Awa},
     title = {Euler scheme for {SDEs} with {non-Lipschitz} diffusion coefficient : strong convergence},
     journal = {ESAIM: Probability and Statistics},
     pages = {1--11},
     year = {2008},
     publisher = {EDP-Sciences},
     volume = {12},
     doi = {10.1051/ps:2007030},
     mrnumber = {2367990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007030/}
}
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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

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