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.
"Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions." Ann. Probab. 44 (1) 399 - 443, January 2016. https://doi.org/10.1214/14-AOP977