The Annals of Probability

Volume growth and escape rate of Brownian motion on a complete Riemannian manifold

Elton P. Hsu and Guangnan Qin

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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.

Article information

Source
Ann. Probab., Volume 38, Number 4 (2010), 1570-1582.

Dates
First available in Project Euclid: 8 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1278593960

Digital Object Identifier
doi:10.1214/09-AOP519

Mathematical Reviews number (MathSciNet)
MR2663637

Zentralblatt MATH identifier
1200.58022

Subjects
Primary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Keywords
Complete Riemannian manifold volume growth Brownian motion escape rate

Citation

Hsu, Elton P.; Qin, Guangnan. Volume growth and escape rate of Brownian motion on a complete Riemannian manifold. Ann. Probab. 38 (2010), no. 4, 1570--1582. doi:10.1214/09-AOP519. https://projecteuclid.org/euclid.aop/1278593960


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References

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