Harnack inequality for subordinate random walks

Ante Mimica, Stjepan Sebek

Research output: Contribution to journalArticleResearchpeer-review

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

Fingerprint

Harnack Inequality
Green's function
Random walk
Bernstein Function
Subordinator
Harmonic Functions
Transition Probability
Laplace
Ball
Non-negative
Exponent
Scaling
Integer
Zero
Estimate
Class
Transition probability

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Harnack inequality for subordinate random walks. / Mimica, Ante; Sebek, Stjepan.

In: Journal of theoretical probability, Vol. 32, No. 2, 06.2019, p. 737-764.

Research output: Contribution to journalArticleResearchpeer-review

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