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
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