Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions
Probability
2019-07-02 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 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.
Keywords
Cite
@article{arxiv.1907.00171,
title = {Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions},
author = {Xi Geng and Cheng Ouyang and Samy Tindel},
journal= {arXiv preprint arXiv:1907.00171},
year = {2019}
}