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

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

2010-10-18

arxiv.org/abs/1010.3596v1

Annals of Probability 2010, Vol. 38, No. 4, 1570-1582

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AOP519 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP519

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.

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