License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2022.15
URN: urn:nbn:de:0030-drops-161016
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16101/
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Nessmann, Andreas

Polyharmonic Functions in the Quarter Plane

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LIPIcs-AofA-2022-15.pdf (0.7 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{nessmann:LIPIcs.AofA.2022.15,
  author =	{Nessmann, Andreas},
  title =	{{Polyharmonic Functions in the Quarter Plane}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16101},
  URN =		{urn:nbn:de:0030-drops-161016},
  doi =		{10.4230/LIPIcs.AofA.2022.15},
  annote =	{Keywords: Polyharmonic functions, Functional equations, Lattice paths, Random walks, Brownian motion, Generating functions, Laplace transforms}
}

Keywords: Polyharmonic functions, Functional equations, Lattice paths, Random walks, Brownian motion, Generating functions, Laplace transforms
Collection: 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)
Issue Date: 2022
Date of publication: 08.06.2022


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