Translator Disclaimer
2019 Discrete harmonic functions in Lipschitz domains
Sami Mustapha, Mohamed Sifi
Electron. Commun. Probab. 24: 1-15 (2019). DOI: 10.1214/19-ECP259

Abstract

We prove the existence and uniqueness of a discrete nonnegative harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed when leaving a globally Lipschitz domain in $\mathbb{Z} ^{d}$. Our method is based on a systematic use of comparison arguments and discrete potential-theoretical techniques.

Citation

Download Citation

Sami Mustapha. Mohamed Sifi. "Discrete harmonic functions in Lipschitz domains." Electron. Commun. Probab. 24 1 - 15, 2019. https://doi.org/10.1214/19-ECP259

Information

Received: 2 January 2019; Accepted: 25 July 2019; Published: 2019
First available in Project Euclid: 18 September 2019

zbMATH: 1422.60076
MathSciNet: MR4017132
Digital Object Identifier: 10.1214/19-ECP259

Subjects:
Primary: 31C35, 60G50
Secondary: 30F10, 60G40

JOURNAL ARTICLE
15 PAGES


SHARE
Back to Top