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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference4 articles.
1. Investigation of waiting time problems by reduction to Markov processes
2. Isham V. and Westcott M. (1978) A self-correcting point process. Submitted for publication.
3. Some properties of counts of events for certain types of point process;Lewis;J. R. Statist. Soc.,1964
4. Central limit analogues for Markov population processes (with discussion);Mcneil;J. R. Statist. Soc.,1973
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