, Volume 271, Issue 3-4, pp 1211-1239
Date: 08 Jul 2011

On stochastic completeness of jump processes

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We prove the following sufficient condition for stochastic completeness of symmetric jump processes on metric measure spaces: if the volume of the metric balls grows at most exponentially with radius and if the distance function is adapted in a certain sense to the jump kernel then the process is stochastically complete. We use this theorem to prove the following criterion for stochastic completeness of a continuous time random walk on a graph with a counting measure: if the volume growth with respect to the graph distance is at most cubic then the random walk is stochastically complete, where the cubic volume growth is sharp.