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Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences
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  • Published: December 1994

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

  • Xue-Mei Li1 

Probability Theory and Related Fields volume 100, pages 417–428 (1994)Cite this article

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  • 16 Citations

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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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Author information

Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Conventry, UK

    Xue-Mei Li

Authors
  1. Xue-Mei Li
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Additional information

Research supported by SERC grant GR/H67263

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Cite this article

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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  • Received: 07 February 1994

  • Revised: 21 December 1994

  • Issue Date: December 1994

  • DOI: https://doi.org/10.1007/BF01268987

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Mathematical Subject Classification

  • 60H10
  • 60H30
  • 53C21
  • 58G32
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