TY - JOUR

T1 - The compensation approach for walks with small steps in the quarter plane

AU - Adan, I.J.B.F.

AU - Leeuwaarden, van, J.S.H.

AU - Raschel, K.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

U2 - 10.1017/S0963548312000594

DO - 10.1017/S0963548312000594

M3 - Article

VL - 22

SP - 161

EP - 183

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

SN - 0963-5483

IS - 2

ER -