Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions

Abstract

In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise, our study encompasses all parameters $H\in (0,1)$, while the multidimensional case is restricted to the case $H>1/2$. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.

Published at http://dx.doi.org/10.1214/14-AOP977 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Smoothness of the density for solutions to Gaussian rough differential equations
• Lower bounds for the density of locally elliptic Itô processes