AI 中文总结
研究由α - 赫尔德路径驱动的粗糙微分方程解的全局先验估计，利用系数及其导数特定组合的利普希茨连续性，通过广义泰勒展开余项的封闭公式来实现。
AI 中文摘要
在本文中，我们在系数及其导数的特定组合（称为基本微分）具有利普希茨连续性（但无界性和强制性）的假设下，建立了由α - 赫尔德路径驱动的一般粗糙微分方程解的全局先验估计，其中α∈(0,1)。我们的主要工具是广义泰勒展开余项的封闭公式，它能以最优方式利用抵消项。
英文摘要
In this article we establish global a priori estimates on the solution of a generic rough differential equation driven by an $α$-Hölder path covering the full range of regularity $α\in(0,1)$, under the hypothesis of Lipschitz continuity (but neither boundedness nor coercivity) of specific combinations of the coefficients and their derivatives, called elementary differentials. Our main tool is a closed formula for the remainder of a generalised Taylor expansion in terms of products of gradients of the elementary differentials, which allows to take advantage of cancellations in an optimal way.
