论文标题
由布朗运动驱动的微分方程的精确局部估计值：低纤维化情况
Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Hypoelliptic Case
论文作者
论文摘要
本文与随机微分方程有关，该方程是由$ d $尺寸的分数布朗尼运动带有hurst参数$ h> 1/4 $的，在粗糙的路径感中被理解。每当方程的系数满足均匀的低纤维化条件时，我们就会对相关的控制距离函数建立尖锐的局部估计，并对溶液密度进行急剧的局部较低估计。我们的方法在很大程度上依赖于方程的粗糙路径结构。
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.
