Coupling and population dependence in branching processes
There are considered general, abstract multitype supercritical branching processes, where individual reproduction may be affected by properties of the whole population, such as its size or history. There is focused the situation upon that where reproduction tends to decrease as population grows, the limiting individual reproductions being those of a traditional (population independent) supercritical branching process. There are found conditions for the population dependence not to matter so that asymptotically, classical Malthusian growth shows up with the same parameters as those of limiting population where individuals reproduce independently, once they have been born into the population and obtained their types. For investigations there are defined imaginary types of particles. The idea is to couple actual and imaginary reproductions of individuals and to extend the methods of \textit{P. Jagers} in his papers [Stochastic Processes Appl. 32, No. 2, 183-212 (1989; Zbl 0678.92009)] and [Classical and modern branching processes. IMA Vol. Math. Appl. 84, 127-139 (1997; Zbl 0867.60062)]. There are made some applications to a tumor model with quiescence.
scientific article; zbMATH DE number 1051763