A stationary distribution for the growth of a population subject to random catastrophes
The problem of the existence of a stationary distribution and the convergence towards it in a certain semistochastic model for the growth of a population is considered. It is assumed that the population grows according to a deterministic equation, but at certain times there are catastrophes, which lead to a decrease in the population level. The hazard function for the occurrence of catastrophes is a function of the population level only. The size of these jumps have a distribution that depends on the population size immediately before the catastrophe. A constructive method for finding the stationary distribution is given.