Stochastic incompleteness for graphs and weak Omori-Yau maximum principle
type: Item
instance of: scholarly article
title: Stochastic incompleteness for graphs and weak Omori-Yau maximum principle
zbMATH Open document ID: 1229.60088
author: Xueping Huang
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-04-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.2579
review text: Consider on a graph \(V\) a Laplacian of type \[ \Delta u(x)={1\over\mu(x)}\sum_yb(x,y)(u(x)-u(y)). \] It is associated to a continuous-time Markov chain on \(V\), and one wonders whether \(V\) is stochastically complete (the Markov chain does not explode in finite time). A necessary and sufficient condition which is an analogue of the weak Omori-Yau condition is given, and some sufficient conditions for stochastic completeness are deduced. The case where \(\mu\equiv1\), and \(b(x,y)\) is 1 if \(x\) and \(y\) are neighbours and 0 otherwise is studied in more detail, with also criteria for stochastic incompleteness. This work unifies previously known criteria.
reviewed by: Jean Picard
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 5880887
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: graphs
zbMATH Keywords: stochastic completeness
zbMATH Keywords: weak Omori-Yau maximum principle
MaRDI profile type: Publication
OpenAlex ID: W2963773741
arXiv ID: 1009.2579
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DOI: 10.1016/J.JMAA.2011.02.009
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