Abstract
We consider a diffusion process {x(t)} on a compact Riemannian manifold with generator δ/2 + b. A current‐valued continuous stochastic process {X t} in the sense of Ito [8] corresponds to {x(t)} by considering the stochastic line integral X t(a) along {x(t)} for every smooth 1-form a. Furthermore {X t} is decomposed into the martingale part and the bounded variation part as a current-valued continuous process. We show the central limit theorems for {X t} and the martingale part of {X t}. Occupation time laws for recurrent diffusions and homogenization problems of periodic diffusions are closely related to these theorems
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