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Limit theorems for processes of randomly displaced regular events

Published online by Cambridge University Press:  14 July 2016

P. S. Collings
P. S. Collings*
Affiliation:
University of Sheffield
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Abstract

Two types of limit theorems are proved for processes of randomly displaced regular events. Firstly, as the displacements tend to infinity, the counting process is shown to converge weakly to a Poisson process and secondly, as the interval between events tends to zero, convergence of the finite-dimensional distributions of the associated storage process to a diffusion is proved.

Keywords

POINT PROCESSSTORAGE MODELWEAK CONVERGENCEPOISSON PROCESSDIFFUSION APROXIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 530 - 537
Copyright
Copyright © Applied Probability Trust 1976 

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