Author:
ADAN IVO J. B. F.,van LEEUWAARDEN JOHAN S. H.,RASCHEL KILIAN
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+2with a step set that is a subset of\[ \{(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)\}\]in the interior of+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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
4 articles.
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