Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case

Abstract

This article is concerned with stochastic differential equations driven by a d-dimensional fractional Brownian motion with Hurst parameter \(H>1/4\), understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform ellipticity 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.