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Article Dans Une Revue Electronic Communications in Probability Année : 2015

Discrete harmonic functions on an orthant in Zd

Résumé

We give a positive answer to a conjecture on the uniqueness of harmonic functions in the quarter plane stated by K. Raschel. More precisely we prove the existence and uniqueness of a positive discrete harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed at the boundary of an orthant in Zd. Our methodsallow on the other hand to generalize from the quarter plane to orthants in higher dimensions and to treat the spatially inhomogeneous walks.
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hal-01214538 , version 1 (12-10-2015)

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Aymen Bouaziz, Sami Mustapha, Mohamed Sifi. Discrete harmonic functions on an orthant in Zd. Electronic Communications in Probability, 2015, 20, pp.1-13. ⟨10.1214/ECP.v20-4249⟩. ⟨hal-01214538⟩
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