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Convergence of martingales on a Riemannian manifold. (English) Zbl 0532.58033

When the scalar quadratic variation of a martingale on a Riemannian manifold is finite almost surely, then the martingale converges almost surely in the one-point compactification of the manifold. A partial converse due to Zheng Weian is also proved. No curvature conditions on the manifold are required.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
60G17 Sample path properties
60G48 Generalizations of martingales
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References:

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