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.

This preprint is the result of splitting our original submission arXiv:1907.00171, which was slightly too long. The current preprint contains the elliptic part of our analysis