Random Walks Associated with Non-Divergence Form Elliptic Equations

Joseph G. Conlon, Renming Song

Research output: Contribution to journalArticlepeer-review


This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d ≥ 2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d - 1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d - 1 dimensional manifolds which are C1, α, and also d - 1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion.

Original languageEnglish (US)
Pages (from-to)427-489
Number of pages63
JournalJournal of Theoretical Probability
Issue number2
StatePublished - 2000


  • Diffusion process
  • Elliptic operator
  • Lipschitz manifolds
  • Random walks

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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