### Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences. (arXiv:1911.07900v1 [math.PR])

In this paper we discuss the stability of stochastic differential equations and the interplay between the moment stability of a SDE and the topology of the underlying manifold. Sufficient and necessary conditions are given for the moment stability of a SDE in terms of the coefficients. Finally we prove a vanishing result for the fundamental…