On stochastic completeness of jump processes

Alexander Grigor'yan, Xueping Huang, Jun Masamune

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1211-1239
Number of pages29
JournalMathematische Zeitschrift
Volume271
Issue number3-4
DOIs
Publication statusPublished - 2012 Aug 1

Keywords

  • Jump processes
  • Non-local Dirichlet forms
  • Physical Laplacian
  • Random walks
  • Stochastic completeness

ASJC Scopus subject areas

  • Mathematics(all)

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