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| HAL : hal-00331845, version 3 |
| arXiv : 0810.3224 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (17-10-2008) | v2 (09-06-2009) | v3 (22-01-2010) |
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| Weak Error for stable driven SDEs: expansion of the densities |
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| Valentin Konakov 1Stephane Menozzi 2 |
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| (17/10/2008) |
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| 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. |
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| 1 : | Central economics Mathematical institute (CMI RAS) |
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Russian Academy of Science |
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| 2 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| Domaine | : | Mathématiques/Probabilités |
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| Symmetric stable processes – parametrix – Euler scheme |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00331845, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00331845 | |
| oai:hal.archives-ouvertes.fr:hal-00331845 | |
| Contributeur : Stephane Menozzi | |
| Soumis le : Vendredi 22 Janvier 2010, 16:05:52 | |
| Dernière modification le : Vendredi 22 Janvier 2010, 16:41:12 | |
