Abstract
A multidimensional version of an age-dependent branching process of Bellman and Harris is studied. In the Introduction the model is described and some of its biological limitations are discussed; in Section 2 it is shown that the mean functions of the process satisfy a system of linear integral equations of the renewal type, and a solution to the system of integral equations is obtained; and in Section 3 the limiting behavior of the mean functions is studied. The analytic techniques used rely heavily on the theory of the Laplace transform and the Perron-Frobenius theory of positive matrices. Further analytic results as well as applications to the theory of natural selection will be developed in a companion article.
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