Convergence of symmetric Markov chains on ℤd

Richard F. Bass, Takashi Kumagai, Toshihiro Uemura

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


For each n let Yt(n) be a continuous time symmetric Markov chain with state space n-1d. Conditions in terms of the conductances are given for the convergence of the Yt(n)t to a symmetric Markov process Yt on ℝd. We have weak convergence of {Yt(n)}: t ≤ t0} for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps.

Original languageEnglish
Pages (from-to)107-140
Number of pages34
JournalProbability Theory and Related Fields
Issue number1
Publication statusPublished - 2010
Externally publishedYes


  • Central limit theorem
  • Dirichlet forms
  • Elliptic diffusions
  • Markov chains
  • Non-local
  • Symmetric
  • Weak convergence

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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