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Zbl 0861.58050
Darling, R.W.R.
Martingales on noncompact manifolds: Maximal inequalities and prescribed limits. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 32, No.4, 431-454 (1996). ISSN 0246-0203

For $\Gamma$-martingales, with respect to an arbitrary connection $\Gamma$ on a Riemannian manifold, a version of the Burkholder-Davis-Gundy inequalities is presented. These are applied to the extension to noncompact manifolds of Kendall's theorem on existence and uniqueness of $\Gamma$-martingales with a prescribed limit, which is related to the Dirichlet problem for harmonic maps.
[S.Eloshvili (Tbilisi)]

MSC 2000:: *58J65 Diffusion processes and stochastic analysis on manifolds
60G48 Generalizations of martingales
60H20 Stochastic integral equations

Keywords: martingales on manifolds; Brownian motion; gamma-martingale

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