JournalsprimsVol. 19, No. 2pp. 753–763

Convergence of Martingales on a Riemannlan Manifold

  • Richard W.R. Darling

    University of Southern California, Los Angeles, USA
Convergence of Martingales on a Riemannlan Manifold cover
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Abstract

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.

Cite this article

Richard W.R. Darling, Convergence of Martingales on a Riemannlan Manifold. Publ. Res. Inst. Math. Sci. 19 (1983), no. 2, pp. 753–763

DOI 10.2977/PRIMS/1195182450