Abstract : Consider a multidimensional SDE of the form $X_t = x+\int_{0}^{t} b(X_{s-})ds+\int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{s\ge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the above equation admits a density w.r.t. the Lebesgue measure and so does its Euler scheme. Using a parametrix approach, we derive an error expansion at order 1 w.r.t. the time step for the difference of these densities.
https://hal.archives-ouvertes.fr/hal-00331845
Contributeur : Stephane Menozzi
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Soumis le : vendredi 22 janvier 2010 - 16:05:52
Dernière modification le : mercredi 21 mars 2018 - 18:56:48
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 18:15:13
