Abstract
Consider an age-dependent branching process with two types of individuals. Suppose that individuals of one type beget children of both types, whereas those of the other type can only give birth to individuals of their own kind. This paper is a study of the relation between two random functions occurring in such processes starting from an ancestor of the first type, the two functions being the numbers of individuals of the two kinds. Under weak assumptions it is shown that the random proportion of individuals of one type converges as time passes, in mean square as well as almost surely to a non-random limit, easily determined in terms of the reproduction laws and life-length distributions of the process.
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