A class of branching processes with two dependent types

We propose a stochastic process model for a population of individuals of two types. Type-I individuals immigrate at the times of a Poisson process and have an arbitrary life time distribution. During their lives they generate type-II individuals, which for themselves may multiply and die. In contrast to classic branching processes they may have an influence on the life time of their type-I ancestor. Conversely at the death of the type-I ancestor all its type-II descendants die simultaneously. We derive the distributions of the relevant random variables and give conditions for the existence of limiting distributions. Finally some examples will be discussed.