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 work we construct stochastic flows associated with the SDEs by using rough path theory, which is something like a 'deterministic version' of Ito's SDE theory.
This is joint work with Kiyotaka Suzaki.
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