Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences

Xue-Mei Li

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arXiv · 1911.07900

Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences

Xue-Mei Li

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Abstract

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 group of a complete Riemannian manifold in terms of purely geometrical quantities.

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Xue-Mei Li. 2019-11-18. Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences. https://arxiv.org/abs/1911.07900

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