Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Hypoelliptic Case
Abstract
This article is concerned with stochastic differential equations driven by a dimensional fractional Brownian motion with Hurst parameter , 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.
Cite
@article{arxiv.2008.01229,
title = {Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Hypoelliptic Case},
author = {Xi Geng and Cheng Ouyang and Samy Tindel},
journal= {arXiv preprint arXiv:2008.01229},
year = {2020}
}
Comments
This preprint is the result of splitting our original submission arXiv:1907.00171, which was slightly too long. The current preprint contains the hypoelliptic part of our analysis. Part of the presentation (and arguments) in the current preprint is different from the original submission