Stochastic completeness and honesty


We show the equivalence of two notions, namely honesty of a semigroup and stochastic completeness of a graph. Honesty occurs in the study of positive perturbations of substochastic semigroups, while stochastic completeness occurs in the study of the heat equation on graphs. We then look at some applications of honesty theory to graphs.

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Correspondence to Chin Pin Wong.

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Wong, C.P. Stochastic completeness and honesty. J. Evol. Equ. 15, 961–978 (2015).

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Mathematics Subject Classification

  • 47D06
  • 47D07
  • 60J27


  • Substochastic semigroups
  • Stochastic completeness
  • Honesty