The growth and spread of the general branching random walk

by J.D.Biggins

Annals of Applied Probability, (1995) 5, 1008-1024.

1991 Mathematics Subject Classification: 60J80


A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behaviour 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.


postscript file

dvi file

See also the companion paper

Other publications by J.D. Biggins

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