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 hypothesis on the manifold, so-called manifolds of bounded geometry. Furthermore, we provide stochastic flow estimates for the solutions.