## The growth and spread of the general branching random walk.(English)Zbl 0859.60075

This is a companion paper to [the author, in: Classical and modern branching processes (ed. Athreya and Jagers, Springer, New York (1996)]. A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behavior of the numbers present at time $$t$$ in sets of the form $$[ta,\infty)$$ is obtained. As a consequence it is shown that if $$B_t$$ is the position of the rightmost person at time $$t$$, $$B_t/t$$ converges to a constant, which can be obtained from the individual reproduction law, almost surely on the survival set of the process. This generalizes the known discrete-time results.
Reviewer: M.Quine (Sydney)

### MSC:

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