Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this paper we construct stochastic flows associated with the SDEs by using rough path theory, which is something like a “deterministic version” of Itô's SDE theory.

中文翻译：

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叶空间上的随机流和粗糙微分方程

紧凑叶面空间上的随机微分方程（SDE）于几年前引入。作为推论，获得了紧凑叶状空间上的叶向布朗运动作为SDE的解决方案。在本文中，我们使用粗糙路径理论来构造与SDE相关的随机流，这类似于ItôSDE理论的“确定性版本”。