Stochastic flows and rough differential equations on foliated spaces

TL;DR

This paper develops a framework for constructing stochastic flows on foliated spaces using rough path theory, extending the understanding of stochastic differential equations in complex geometric settings.

Contribution

It introduces a novel approach to build stochastic flows on foliated spaces via rough path theory, bridging stochastic analysis and geometric structures.

Findings

Constructed stochastic flows on foliated spaces using rough path theory.

Extended SDE solutions to complex geometric settings.

Provided a deterministic approach to stochastic flows on foliated structures.

Abstract

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 It\^o's SDE theory.