Polyharmonic Functions in the Quarter Plane

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. 2012 ACM Subject Classification Theory of computation → Random walks and Markov chains; Mathematics of computing → Markov processes; Mathematics of computing → Generating functions; Mathematics of computing → Combinatorics Acknowledgements I would like to thank Kilian Raschel for introducing me to this topic as well as for a lot of valuable input and many fruitful discussions. Also, I would like to thank the anonymous reviewers for their valuable remarks.