Martingales on noncompact manifolds: Maximal inequalities and prescribed limits
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.
scientific article; zbMATH DE number 915913