Stochastic completeness and volume growth
Differential Geometry
2010-04-02 v2 Probability
Abstract
It has been suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counter-examples to a converse implication.
Cite
@article{arxiv.0908.4222,
title = {Stochastic completeness and volume growth},
author = {Christian Baer and G. Pacelli Bessa},
journal= {arXiv preprint arXiv:0908.4222},
year = {2010}
}
Comments
11 pages, 5 figures, published version