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On a class of two-dimensional nearest-neighbour random walks

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

J. W. Cohen
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Abstract

For positive recurrent nearest-neighbour, semi-homogeneous random walks on the lattice {0, 1, 2, …} X {0, 1, 2, …} the bivariate generating function of the stationary distribution is analysed for the case where one-step transitions to the north, north-east and east at interior points of the state space all have zero probability. It is shown that this generating function can be represented by meromorphic functions. The construction of this representation is exposed for a variety of one-step transition vectors at the boundary points of the state space.

Keywords

STATIONARY DISTRIBUTIONSEMI-HOMOGENEOUSGENERATING FUNCTIONMEROMORPHIC FUNCTIONS

MSC classification

Secondary: 60K25: Queueing theory
Type
Part 4 Random Walks
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 207 - 237
Copyright
Copyright © Applied Probability Trust 1994 

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