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Limit theorems for processes of randomly displaced regular events
P. S. Collings
Journal:

Journal of Applied Probability / Volume 13 / Issue 3 / September 1976

Published online by Cambridge University Press:

14 July 2016, pp. 530-537

Print publication:

September 1976
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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.

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Limit theorems for processes of randomly displaced regular events