Stochastic flows and rough differential equations on foliated spaces
Dynamical Systems
2020-03-05 v2 Probability
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.
Cite
@article{arxiv.1910.09962,
title = {Stochastic flows and rough differential equations on foliated spaces},
author = {Yuzuru Inahama and Kiyotaka Suzaki},
journal= {arXiv preprint arXiv:1910.09962},
year = {2020}
}
Comments
Final version. Minor errors were corrected. 24 pages. To appear in Bull. Sci. Math