Harnack inequality for subordinate random walks

Ante Mimica; Stjepan Sebek

doi:10.1007%2Fs10959-018-0821-5

Harnack inequality for subordinate random walks

Ante Mimica, Stjepan Sebek

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider a large class of subordinate random walks X on the integer lattice 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.

Original language	English
Pages (from-to)	737-764
Number of pages	28
Journal	Journal of Theoretical Probability
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007%2Fs10959-018-0821-5
Publication status	Published - Jun 2019
Externally published	Yes

Keywords

Random walk
Subordination
Harnack inequality
Harmonic function
Green function
Poisson kernel

ASJC Scopus subject areas

General Mathematics

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10.1007%2Fs10959-018-0821-5

https://link.springer.com/article/10.1007%2Fs10959-018-0821-5

Cite this

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title = "Harnack inequality for subordinate random walks",

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.",

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author = "Ante Mimica and Stjepan Sebek",

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AU - Mimica, Ante

AU - Sebek, Stjepan

PY - 2019/6

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AB - 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.

KW - Random walk

KW - Subordination

KW - Harnack inequality

KW - Harmonic function

KW - Green function

KW - Poisson kernel

U2 - 10.1007%2Fs10959-018-0821-5

DO - 10.1007%2Fs10959-018-0821-5

M3 - Article

SN - 1572-9230

VL - 32

SP - 737

EP - 764

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 2

ER -

Harnack inequality for subordinate random walks

Abstract

Keywords

ASJC Scopus subject areas

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