2026-08-16T16:41:24Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16101 2024-03-06T10:56:57Z ddc:004 open_access

Polyharmonic Functions in the Quarter Plane Nessmann, Andreas Polyharmonic functions Functional equations Lattice paths Random walks Brownian motion Generating functions Laplace transforms In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic functions, and convergence between the discrete and continuous cases is shown. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andreas Nessmann 2022 Is Part Of LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2022.15 urn:nbn:de:0030-drops-161016 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.15 eng https://creativecommons.org/licenses/by/4.0/legalcode