Comptes Rendus
no. 7
Probability theory
Existence and Besov regularity of the density for a class of SDEs with Volterra noise

Presented by: the Editorial Board

Christian Olivera1; Ciprian A. Tudor2, 3
1 Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970, Campinas – SP, Brazil
2 Université de Lille-1, CNRS, UMR 8524, Laboratoire Paul-Painlevé, 59655 Villeneuve-d'Ascq, France
3 ISMMA, Romanian Academy, Bucharest, Romania
Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 636-645.

By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak regularity conditions on the drift. Several examples of Gaussian Volterra noises are discussed.

En utilisant une méthode simple basée sur l'intégration fractionnelle par parties, nous prouvons l'existence et la régularité de Besov de la densité des solutions des équations différentielles stochastiques dirigées par un bruit additif gaussien de type Volterra. Nous supposons des conditions de faible régularité sur le coefficient de dérive. Plusieurs exemples de bruits gaussiens de Volterra sont discutés.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.06.012

Christian Olivera 1; Ciprian A. Tudor 2, 3

1 Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970, Campinas – SP, Brazil
2 Université de Lille-1, CNRS, UMR 8524, Laboratoire Paul-Painlevé, 59655 Villeneuve-d'Ascq, France
3 ISMMA, Romanian Academy, Bucharest, Romania 
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Christian Olivera; Ciprian A. Tudor. Existence and Besov regularity of the density for a class of SDEs with Volterra noise. Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 636-645. doi : 10.1016/j.crma.2019.06.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.06.012/

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