Upper escape rate of Markov chains on weighted graphs

Xueping Huang and Yuichi Shiozawa

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 317-347

Abstract: We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain defined on a locally finite weighted graph. This upper rate function, which has the same form as the manifold setting, is given in terms of the volume growth with respect to an adapted path metric. Our approach also gives a weak form of Folz’s theorem on the conservativeness as a consequence.

Keywords: Escape rate; Upper rate function; Markov chains; Weighted graphs (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2013.08.004

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