no. 7
Probability theory
Existence and Besov regularity of the density for a class of SDEs with Volterra noise
[Existence et régularité de Besov de la densité pour une classe d'équations différentielles stochastiques avec bruit de Volterra]

Présenté par : the Editorial Board

Olivera, Christian1 ; Tudor, Ciprian A.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
Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 636-645.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2019.06.012
Olivera, Christian 1 ; Tudor, Ciprian A. 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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Olivera, Christian; Tudor, Ciprian A. Existence and Besov regularity of the density for a class of SDEs with Volterra noise. Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 636-645. doi : 10.1016/j.crma.2019.06.012. http://www.numdam.org/articles/10.1016/j.crma.2019.06.012/

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