Abstract

This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter H>1/4 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.

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