Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T04:04:51.024Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  14 July 2016

D. R. Cox  and
V. Isham
D. R. Cox
Affiliation:
Imperial College London
V. Isham
Affiliation:
Imperial College London
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

BIRTH PROCESSCONTROLLED VARIABILITYDIFFUSIONPOINT PROCESSTAKÁCS PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 610 - 616
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Isham, V. and Westcott, M. (1978) A self-correcting point process. Submitted for publication.Google Scholar
Lewis, T. and Govier, L. J. (1964) Some properties of counts of events for certain types of point process. J. R. Statist. Soc. B 26, 325–337.Google Scholar
Mcneil, D. R. and Schach, S. (1973) Central limit analogues for Markov population processes (with discussion). J. R. Statist. Soc. B 35, 1–23.Google Scholar
Takács, L. (1955) Investigation of waiting time problems by reduction to Markov processes. Acta. Math. Acad. Sci. Hungar. 6, 101–129.Google Scholar