The density of the extinction probability of a time homogeneous linear birth and death process under the influence of randomly occurring disasters (Q1569922)

The paper considers a continuous-time birth and death process whereas disasters can occur randomly that diminish the population. The disasters happen according to a renewal process and the number of survivors is binomially distributed with killing rate \(\varepsilon\). The extinction probability \(q\) of the process is a random variable and the aim of the paper is to derive an integral expression for the probability density function of \(q\) for a time-homogeneous linear birth and death process. In an example it is demonstrated how to evaluate the integral numerically.