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

Baudoin, Fabrice; Nualart, Eulàlia; Ouyang, Cheng; Tindel, Samy

doi:http://dx.doi.org/10.1214/15-AOP1028

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

Citation

Baudoin F, Nualart E, Ouyang C, Tindel S. On probability laws of solutions to differential systems driven by a fractional Brownian motion. Ann Probab. 2016;44(4):2554-90. DOI: 10.1214/15-AOP1028

Abstract

This article investigates several properties related to densities of solutions (Xt)t∈[0,1] 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 Xt. 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.