The compensation approach for walks with small steps in the quarter plane

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Abstract

This paper is the first application of the compensation approach (a well-established theory in probability theory) to counting problems. We discuss how this method can be applied to a general class of walks in the quarter plane + 2 with a step set that is a subset of {(-1,1),(-1,0),(0,-1),(1,-1)} in the interior of $Z^2_+$. We derive an explicit expression for the generating function which turns out to be non-holonomic, and which can be used to obtain exact and asymptotic expressions for the counting numbers.
Original languageEnglish
Pages (from-to)161-183
JournalCombinatorics, Probability and Computing
Volume22
Issue number2
DOIs
Publication statusPublished - 2013

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