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

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.(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.