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Limiting angle of Brownian motion on certain manifolds
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  • Published: September 1996

Limiting angle of Brownian motion on certain manifolds

  • Huiling Le1 

Probability Theory and Related Fields volume 106, pages 137–149 (1996)Cite this article

Summary.

Suppose that M is a complete, simply connected Riemannian manifold of non-positive sectional curvature with dimension m ≧ 3. If, outside a fixed compact set, the sectional curvatures are bounded above by a negative constant multiple of the inverse of the square of the geodesic distance from a fixed point and below by another negative constant multiple of the square of the geodesic distance, then the angular part of Brownian motion on M tends to a limit as time tends to infinity, and the closure of the support of the distribution of this limit is the entire S m−1. This improves a result of Hsu and March.

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Authors and Affiliations

  1. University of Nottingham, Department of Mathematics, University Park, Nottingham NG7 2RD, UK, , , , , , GB

    Huiling Le

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  1. Huiling Le
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Received: 7 December 1994/In revised form: 2 September 1995

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Le, H. Limiting angle of Brownian motion on certain manifolds. Probab Theory Relat Fields 106, 137–149 (1996). https://doi.org/10.1007/s004400050060

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  • Issue Date: September 1996

  • DOI: https://doi.org/10.1007/s004400050060

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  • Mathematics Subject Classification (1991): 60G65
  • 58G32
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