A practical global existence and uniqueness result for stochastic differential equations on Riemannian manifolds of bounded geometry

Abstract

In this paper, we establish a result for existence and uniqueness of stochastic differential equations on Riemannian manifolds, for regular inhomogeneous tensor coefficients with stochastic drift, under geometrical-only hypothesis on the manifold, so-called manifolds of bounded geometry, this hypothesis is consistent with the maximal regularity result for parabolic equations obtained by Herbert Amann. Furthermore, we provide a stochastic flow estimate for the solutions.