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Journal of Theoretical Probability

, Volume 32, Issue 2, pp 737–764 | Cite as

Harnack Inequality for Subordinate Random Walks

  • Ante Mimica
  • Stjepan ŠebekEmail author
Article

Abstract

In this paper, we consider a large class of subordinate random walks X on the integer lattice \(\mathbb {Z}^d\) 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.

Keywords

Random walk Subordination Harnack inequality Harmonic function Green function Poisson kernel 

Mathematics Subject Classification (2010)

Primary: 60J45 Secondary: 60G50 60J10 05C81 

Notes

Acknowledgements

This work has been supported in part by Croatian Science Foundation under the project 3526.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.Department of Applied Mathematics, Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia

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