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

TL;DR

This paper proves the existence and uniqueness of solutions to stochastic differential equations on Riemannian manifolds of bounded geometry, including flow estimates, advancing understanding of stochastic processes in geometric contexts.

Contribution

It introduces new existence and uniqueness results for SDEs on manifolds with bounded geometry, incorporating stochastic drifts and tensor coefficients.

Findings

Existence and uniqueness of solutions established

Stochastic flow estimates provided

Applicable to 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.