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arXiv · 0908.4222

Stochastic completeness and volume growth

Christian Baer·G. Pacelli Bessa
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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.

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Christian Baer, G. Pacelli Bessa. 2009-08-28. Stochastic completeness and volume growth. https://doi.org/10.1090/s0002-9939-10-10281-0

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