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The Compensation Approach for Walks With Small Steps in the Quarter Plane

  • IVO J. B. F. ADAN (a1), JOHAN S. H. van LEEUWAARDEN (a1) and KILIAN RASCHEL (a2)

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

\[ \{(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)\}\]
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.

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Keywords

The Compensation Approach for Walks With Small Steps in the Quarter Plane

  • IVO J. B. F. ADAN (a1), JOHAN S. H. van LEEUWAARDEN (a1) and KILIAN RASCHEL (a2)

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