Stochastic completeness and volume growth
arXiv:0908.4222 · doi:10.1090/S0002-9939-10-10281-0
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.
11 pages, 5 figures, published version