Series expansions for the properties of a birth process of controlled variability
- 1 September 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (3) , 610-616
- https://doi.org/10.2307/3213123
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
This publication has 3 references indexed in Scilit:
- Central Limit Analogues for Markov Population ProcessesJournal of the Royal Statistical Society Series B: Statistical Methodology, 1973
- Some Properties of Counts of Events for Certain Types of Point ProcessJournal of the Royal Statistical Society Series B: Statistical Methodology, 1964
- Investigation of waiting time problems by reduction to Markov processesActa Mathematica Hungarica, 1955