The Growth and Spread of the General Branching Random Walk
Biggins, J. D.
Ann. Appl. Probab., Volume 5 (1995) no. 4, p. 1008-1024 / Harvested from Project Euclid
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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 $\lbrack ta, \infty)$ 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.
Published online : 1995-11-14
Classification:  Spatial spread,  asymptotic speed,  propagation rate,  CMJ process,  60J80 
@article{1177004604,
     author = {Biggins, J. D.},
     title = {The Growth and Spread of the General Branching Random Walk},
     journal = {Ann. Appl. Probab.},
     volume = {5},
     number = {4},
     year = {1995},
     pages = { 1008-1024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177004604}
}

Biggins, J. D. The Growth and Spread of the General Branching Random Walk. Ann. Appl. Probab., Volume 5 (1995) no. 4, pp.  1008-1024. http://gdmltest.u-ga.fr/item/1177004604/