Symmetric markov chains on double-struck Z signd with unbounded range

Richard F. Bass, Takashi Kumagai

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We consider symmetric Markov chains on double-struck Z signd where we do not assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper bounds on the transition probabilities, estimates for exit time probabilities, and certain lower bounds on the transition probabilities. We show that a uniform Harnack inequality holds if an additional assumption is made, but that without this assumption such an inequality need not hold. We establish a central limit theorem giving conditions for a sequence of normalized symmetric Markov chains to converge to a diffusion on ℝd corresponding to an elliptic operator in divergence form.

Original languageEnglish
Pages (from-to)2041-2075
Number of pages35
JournalTransactions of the American Mathematical Society
Volume360
Issue number4
DOIs
Publication statusPublished - 2008 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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