This work examines diffusion processes and their relation to the Godbillon-Vey class in Riemannian manifolds, indicating significant theoretical connections.
In this work, we revisit the theory of considering diffusion processes as 1-currents defined by line integrals along their trajectories. Specifically, we will study diffusion processes defined by solutions to stochastic differential equations, with a particular focus on foliated Brownian motion. We will explore the connection between this theory, the Godbillon-Vey class, and the entropy of foliations on compact Riemannian manifolds.
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Diego S. Ledesma (2025) studied this question.
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