A class of branching processes with two dependent types

Eike Born and Klaus Dietz

Stochastic Processes and their Applications, 1990, vol. 36, issue 2, 297-310

Abstract: 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.

Keywords: Two-type; branching; process; depending; types; limiting; distributions (search for similar items in EconPapers)
Date: 1990
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