inria-00000176, version 2
Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
Abdel Berkaoui
1Mireille Bossy 2, 3Awa Diop 2, 3
ESAIM: Probability and Statistics 12 (2008) 15
Résumé : We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |x|^a, a 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.
- 1 : Dept of Statistics, University of Warwick
- University of Warwick
- 2 : Institut Elie Cartan Nancy (IECN)
- CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- 3 : TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
- INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- Domaine : Mathématiques/Analyse numérique
Mathématiques/Probabilités - Mots-clés : Euler scheme – strong error – CIR process – Hull-White process – SABR processes
- Référence interne : RR-5637-V2
- Versions disponibles : v1 (22-07-2005) v2 (10-01-2006)
- inria-00000176, version 2
- http://hal.inria.fr/inria-00000176
- oai:hal.inria.fr:inria-00000176
- Contributeur : Mireille Bossy
- Soumis le : Mardi 10 Janvier 2006, 11:01:47
- Dernière modification le : Mardi 26 Avril 2011, 16:16:56
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