On Stratonovich and Skorohod stochastic calculus for Gaussian processes

Yaozhong Hu (1) , Maria Jolis (2) , Samy Tindel (3, 4)

1 Department of Mathematics [Lawrence, Kansas]
2 UAB - Departament de Matemàtiques [Barcelona]
3 BIGS - Biology, genetics and statistics
4 IECL - Institut Élie Cartan de Lorraine

In this article, we derive a Stratonovich and Skorohod type change of variables formula for a multidimensional Gaussian process with low Hölder regularity (typically lower than 1/4). To this aim, we combine tools from rough paths theory and stochastic analysis.

Keywords: Gaussian processes; rough paths; Malliavin calculus; Itô's formula

Domains: Probability [math.PR]

Yaozhong Hu, Maria Jolis, Samy Tindel. On Stratonovich and Skorohod stochastic calculus for Gaussian processes. Annals of Probability, 2013, 41 (3), pp.1656-1693. ⟨10.1214/12-AOP751⟩. ⟨hal-00556955⟩