MARTINGALES ON NONCOMPACT MANIFOLDS - MAXIMAL INEQUALITIES AND PRESCRIBED LIMITS

A version of the Burkholder-Davis-Gundy inequalities is presented for Gamma-martingales, with respect to an arbitrary connection Gamma on a Riemannian manifold (M, g). Under convexity assumptions on the manifol d, some limit results are derived for ''H-p Gamma-martingales'', i.e. those whose total Riemannian quadratic variation is in L(p/2). These a re applied to the extension to noncompact manifolds of Kendall's theor em on existence and uniqueness of Gamma-martingales with a prescribed limit, which is related to the Dirichlet problem for harmonic maps.