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Upper escape rate of Markov chains on weighted graphs

Author

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  • Huang, Xueping
  • Shiozawa, Yuichi

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.

Suggested Citation

  • Huang, Xueping & Shiozawa, Yuichi, 2014. "Upper escape rate of Markov chains on weighted graphs," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 317-347.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:317-347
    DOI: 10.1016/j.spa.2013.08.004
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