## The Annals of Probability

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

#### Abstract

This article investigates several properties related to densities of solutions $(X_{t})_{t\in[0,1]}$ 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 $X_{t}$. 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.

#### Article information

Source
Ann. Probab., Volume 44, Number 4 (2016), 2554-2590.

Dates
Revised: February 2015
First available in Project Euclid: 2 August 2016

https://projecteuclid.org/euclid.aop/1470139149

Digital Object Identifier
doi:10.1214/15-AOP1028

Mathematical Reviews number (MathSciNet)
MR3531675

Zentralblatt MATH identifier
1352.60081

#### 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. 44 (2016), no. 4, 2554--2590. doi:10.1214/15-AOP1028. https://projecteuclid.org/euclid.aop/1470139149

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