STOCHASTIC-MODEL FOR A REPLICATING POPULATION SUBJECTED TO MASS EMIGRATION DUE TO POPULATION PRESSURE

A model is proposed for a population that is growing exponentially and at certain instants of time undergoes mass emigration due to population size pressure. The numbers emigrating are independently and identically distributed, and the intervals of time between any two emigration times have distributions which are functionals of the history of the population evolution since the last emigration. Some results are given for the time to extinction of the population and its first moment, and also of the evolution of the population level. More details are given when the emigration size distribution is negative exponential. © 1979.