On probability laws of solutions to differential systems driven by a fractional Brownian motion.

Fabrice Baudoin (1) , Eulalia Nualart (2) , Cheng Ouyang (3) , Samy Tindel (4, 5)

1 Department of Mathematics
2 Dept. Economics and Business
3 Dept. Mathematics, Statistics and Computer Science
4 BIGS - Biology, genetics and statistics
5 IECL - Institut Élie Cartan de Lorraine

This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density of X_t. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities.

Mots clés: Malliavin calculus; rough paths; fractional Brownian motion

Domaines: Probabilités [math.PR]

Fabrice Baudoin, Eulalia Nualart, Cheng Ouyang, Samy Tindel. On probability laws of solutions to differential systems driven by a fractional Brownian motion.. [Research Report] non spécifié. 2014. ⟨hal-00931118⟩