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Limit theorems for a class of diffusion processes. (English) Zbl 0583.60073
Author’s abstract: We consider a diffusion process \(\{\) x(t)\(\}\) on a compact Riemannian manifold with generator \(\Delta /2+b\). A current- valued continuous stochastic process \(\{X_ t\}\) corresponds to \(\{\) x(t)\(\}\) by considering the stochastic line integral \(X_ t(\alpha)\) along \(\{\) x(t)\(\}\) for every smooth 1-form \(\alpha\). 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.
Reviewer: S.Eloshvili

MSC:
60J60 Diffusion processes
58J65 Diffusion processes and stochastic analysis on manifolds
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