The growth and spread of the general branching random walk (Q1916481)

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.