Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60-04 Explicit machine computation and programs (not the theory of computation or programming)
- 60J30 Processes with independent increments
- 60H10 Stochastic ordinary differential equations, See Also {

**Résumé:** The Euler scheme is a well-known method of approximation of solutions of stochastic differential equations (SDE). A lot of results are now available concerning the precision of this approximation in case of equations driven by a drift and a Brownian motion. More recently, people got interested in the approximation of solution of SDE's driven by a general L\'evy process. One of the problem when we use L\'evy processes is that we can not simulate them in general and so we can not apply the Euler scheme. We propose here a new method of approximation based on the cutoff of the small jumps of the L\'evy process involved. In order to find the speed of convergence of our approximation, we will use results about stability of the solutions of SDE's.

**Mots Clés:** *Euler scheme ; Lévy process ; stochastic differential equations*

**Date:** 2001-10-24

**Prépublication numéro:** *PMA-695*