On stochastic completeness of jump processes

Alexander Grigor'yan, Xueping Huang, Jun Masamune

研究成果: Article査読

45 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1211-1239
ページ数29
ジャーナルMathematische Zeitschrift
271
3-4
DOI
出版ステータスPublished - 2012 8 1

ASJC Scopus subject areas

  • 数学 (全般)

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