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Sur quelques théorèmes de convergence du processus de naissance avec interaction des voisins. (On some convergence theorems of birth processes with neighbour interactions). (French) Zbl 0624.60096
The standard Galton-Watson process is modified so that within each generation individuals are ordered and the numbers of offspring of these individuals are assumed to be m-dependent random variables. That is, the numbers of offspring of two individuals are independent if the individuals are more than m places apart in the ordering.
Necessary and sufficient conditions are given in order that the process be non-degenerate and that moments exist. A central limit theorem and a law of the iterated logarithm are also established.
Reviewer: D.P.Kennedy

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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