Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case
Probability
2020-08-03 v1
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 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.
Cite
@article{arxiv.2007.16178,
title = {Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case},
author = {Xi Geng and Cheng Ouyang and Samy Tindel},
journal= {arXiv preprint arXiv:2007.16178},
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 elliptic part of our analysis