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