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Series expansions for the properties of a birth process of controlled variability

Published online by Cambridge University Press:  14 July 2016

D. R. Cox
Affiliation:
Imperial College London
V. Isham
Affiliation:
Imperial College London

Abstract

A birth process is studied in which the birth rate at any time is a function of the difference between the current population size and a target corresponding to unit growth rate. If this controlling function is a decreasing function of its argument a stabilizing effect is to be expected. By supposing that the controlling function varies very slowly, series expansions for the properties of the process are obtained, the leading term corresponding to a diffusion approximation. The sequence of births considered as a point process of controlled variability is examined and approximations to the interval distribution and covariance density obtained.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1978 

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References

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