A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes

Abstract

In a class of population-size-dependent Galton-Watson processes where extinction does not occur with probability 1 we describe the rate of decay of qi (the probability that the process starting from i ancestors will become extinct) as the number i of ancestors increases.The results are related to the asymptotic behavior of the Green's function of the critical Galton-Watson process with immigration.