Harnack inequality for subordinate random walks
Abstract
In this paper, we consider a large class of subordinate random walks $X$ on integer lattice $\mathbb{Z}^d$ via subordinators with Laplace exponents which are complete Bernstein functions satisfying a certain lower scaling condition 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 non-negative harmonic functions.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2017
- DOI:
- 10.48550/arXiv.1701.07690
- arXiv:
- arXiv:1701.07690
- Bibcode:
- 2017arXiv170107690M
- Keywords:
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- Mathematics - Probability;
- 60J45
- E-Print:
- 31 pages