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July 2010 Volume growth and escape rate of Brownian motion on a complete Riemannian manifold
Elton P. Hsu, Guangnan Qin
Ann. Probab. 38(4): 1570-1582 (July 2010). DOI: 10.1214/09-AOP519

Abstract

We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work is estimating the small tail probability of the crossing time between two concentric geodesic spheres by reflecting Brownian motions on the larger geodesic ball.

Citation

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Elton P. Hsu. Guangnan Qin. "Volume growth and escape rate of Brownian motion on a complete Riemannian manifold." Ann. Probab. 38 (4) 1570 - 1582, July 2010. https://doi.org/10.1214/09-AOP519

Information

Published: July 2010
First available in Project Euclid: 8 July 2010

zbMATH: 1200.58022
MathSciNet: MR2663637
Digital Object Identifier: 10.1214/09-AOP519

Subjects:
Primary: 58J65

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 4 • July 2010
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