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Tohoku Mathematical Journal
SECOND SERIES VOL. 67, NO. 2
|Tohoku Math. J.|
67 (2015), 247-272
AN SDE APPROACH TO LEAFWISE DIFFUSIONS ON FOLIATED SPACES AND ITS APPLICATIONS
(Received September 27, 2013, revised April 4, 2014)
We construct leafwise diffusions on foliated spaces via SDE approach. The obtained diffusions are stochastically continuous and hence have the Feller property. Moreover our construction enables us to prove a central limit theorem for the leafwise diffusion on a compact foliated space in the same way as for a diffusion on a compact manifold.
Mathematics Subject Classification.
Primary 37C40; Secondary 60J60, 60F05.
Key words and phrases.
Foliated space, leafwise diffusion process, harmonic measure, central limit theorem.
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