@article{BaerBessa2010, author = {B{\"a}r, Christian and Bessa, C. Pacelli}, title = {Stochastic completeness and volume growth}, issn = {0002-9939}, doi = {10.1090/S0002-9939-10-10281-0}, year = {2010}, abstract = {It was 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 counterexamples to a converse implication.}, language = {en} }