Harnack inequality for subordinate random walks

Ante Mimica, Stjepan Sebek

Research output: Contribution to journalArticle

Abstract

In this paper, we consider a large class of subordinate random walks X on the integer lattice Zd via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero. We establish estimates for one-step transition probabilities, the Green function and the Green function of a ball, and prove the Harnack inequality for nonnegative harmonic functions.
Original languageEnglish
Pages (from-to)737-764
Number of pages28
JournalJournal of Theoretical Probability
Volume32
Issue number2
DOIs
Publication statusPublished - Jun 2019
Externally publishedYes

Keywords

  • Random walk
  • Subordination
  • Harnack inequality
  • Harmonic function
  • Green function
  • Poisson kernel

ASJC Scopus subject areas

  • Mathematics(all)

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