论文标题
在Sobolev粗糙路径上
On Sobolev rough paths
论文作者
论文摘要
我们介绍了具有Sobolev的规律性和受控Sobolev路径的相应概念的粗糙路径空间。基于这些概念，我们研究了粗糙的路径整合和粗糙的微分方程。作为主要结果，我们证明了与粗糙路径驱动的微分方程相关的解决方案图是Sobolev粗糙路径空间上的局部Lipschitz连续地图，任何任意的低规律性$α$ and Entighobility $ p $提供$α> 1/p $。
We introduce the space of rough paths with Sobolev regularity and the corresponding concept of controlled Sobolev paths. Based on these notions, we study rough path integration and rough differential equations. As main result, we prove that the solution map associated to differential equations driven by rough paths is a locally Lipschitz continuous map on the Sobolev rough path space for any arbitrary low regularity $α$ and integrability $p$ provided $α>1/p$.
