论文标题
Lipschitz的稳定性是受控的粗糙路径和粗糙的微分方程的稳定性
Lipschitz-stability of Controlled Rough Paths and Rough Differential Equations
论文作者
论文摘要
我们为在受控粗糙路径的框架下提供了对粗糙微分方程的解决方案的存在和独特性的说明。在文献中，当驾驶路径为$β$-Hölder连续$β$-Hölder连续（以$β> 1/3 $）的速度可以使用。在$β\ leqslant1/3的情况下，$的主要挑战和缺失的成分是表明，受控的粗糙路径在与Lipschitz转换的组成下关闭。精确建立这种财产具有强大的代数性质，是本文的主要目的。
We provide an account for the existence and uniqueness of solutions to rough differential equations under the framework of controlled rough paths. The case when the driving path is $β$-Hölder continuous, for $β>1/3$, is widely available in the literature. In its extension to the case when $β\leqslant1/3,$ a main challenge and missing ingredient is to show that controlled roughs paths are closed under composition with Lipschitz transformations. Establishing such a property precisely, which has a strong algebraic nature, is a main purpose of the present article.
