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Some remarks on a One-dimensional skip-free process with repulsion

Part of: Limit theorems

Published online by Cambridge University Press:  09 April 2009

Anthony G. Pakes
Anthony G. Pakes
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia
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Abstract

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We extend the results obtained by Hines and Thompson for a Markov chain which has a single reflecting barrier at the origin, nearest neighbour transitions and which moves from {j} to {j + l} with probability j/(j + 1). Martingale limit theorems are used to work out an asymptotic theory for a general class of such chains for which the probability above has the form l – λ(j) = O>λ(j)>1 (j ∈N),λ(j)→ O (j →∞)and Σλ(j)=∞ We discuss the case where the last sum is finite and some alternative versions of the general case.

MSC classification

Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 107 - 128
Copyright
Copyright © Australian Mathematical Society 1980

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