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arXiv · 1907.00171

Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions

Xi Geng·Cheng Ouyang·Samy Tindel
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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 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.

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Xi Geng, Cheng Ouyang, Samy Tindel. 2019-06-29. Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions. https://arxiv.org/abs/1907.00171

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