Stochastic incompleteness for graphs and weak Omori-Yau maximum principle
arXiv:1009.2579
Abstract
We prove an analogue of the weak Omori-Yau maximum principle and Khas'minskii's criterion for graphs in the general setting of Keller and Lenz. Our approach naturally gives the stability of stochastic incompleteness under certain surgeries of graphs. It allows to develop a unified approach to all known criteria of stochastic completeness/incompleteness, as well as to obtain new criteria.
Revised version. We add some previously omitted proof