Convergence of Martingales on a Riemannlan Manifold
Convergence of Martingales on a Riemannlan Manifold
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 Wei-an is also proved. No curvature conditions on the manifold are required.