Summary
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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Research supported by SERC grant GR/H67263
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Li, XM. Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences. Probab. Th. Rel. Fields 100, 417–428 (1994). https://doi.org/10.1007/BF01268987
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DOI: https://doi.org/10.1007/BF01268987
Mathematical Subject Classification
- 60H10
- 60H30
- 53C21
- 58G32