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In this paper we obtain Gaussian-type lower bounds for the density ofsolutions to stochastic differential equations (SDEs) driven by a fractionalBrownian motion with Hurst parameter $H$. In the one-dimensional case withadditive noise, our study encompasses all parameters $H\in(0,1)$, while themultidimensional case is restricted to the case $H>1/2$. We rely on a mix ofpathwise methods for stochastic differential equations and stochastic analysistools.

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