Stochastic integration with respect to Gaussian processes

Laurent Decreusefond

doi:10.1016/S1631-073X(02)02360-9

Stochastic integration with respect to Gaussian processes
[Intégrale stochastique pour les processus gaussiens]

Laurent Decreusefond ¹

¹ E.N.S.T. 46, rue Barrault, 75634 Paris cedex 13, France

Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 903-908.

Résumé
Abstract

Nous construisons une intégrale stochastique du type Stratonovitch–Skorohod, pour les processus gaussiens généraux. Nous montrons qu'elle peut être approchée par des sommes de type Stratonovitch et nous établissons sa régularité trajectorielle. Nous étudions aussi la façon dont elle se transforme lors d'un changement absolument continu de probabilité. Nous montrons enfin que la formule d'Itô–Stratonovitch est vérifiée.

We construct a Stratonovitch–Skorohod-like stochastic integral for general Gaussian processes. We study its sample path regularity and one of its numerical approximating schemes. We also analyze the way it is transformed by an absolutely continuous change of probability and we give an Itô formula.

Reçu le : 2001-10-07
Accepté le : 2002-03-15
Publié le : 2002-04-18

DOI : 10.1016/S1631-073X(02)02360-9

Affiliations des auteurs :

Laurent Decreusefond ¹

¹ E.N.S.T. 46, rue Barrault, 75634 Paris cedex 13, France

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Laurent Decreusefond. Stochastic integration with respect to Gaussian processes. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 903-908. doi : 10.1016/S1631-073X(02)02360-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02360-9/

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