This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter and understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.
"Precise local estimates for differential equations driven by fractional Brownian motion: Hypoelliptic case." Ann. Probab. 50 (2) 649 - 687, March 2022. https://doi.org/10.1214/21-AOP1542