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November, 1995 The Growth and Spread of the General Branching Random Walk
J. D. Biggins
Ann. Appl. Probab. 5(4): 1008-1024 (November, 1995). DOI: 10.1214/aoap/1177004604

Abstract

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.

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J. D. Biggins. "The Growth and Spread of the General Branching Random Walk." Ann. Appl. Probab. 5 (4) 1008 - 1024, November, 1995. https://doi.org/10.1214/aoap/1177004604

Information

Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0859.60075
MathSciNet: MR1384364
Digital Object Identifier: 10.1214/aoap/1177004604

Subjects:
Primary: 60J80

Keywords: asymptotic speed , CMJ process , propagation rate , Spatial spread

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 4 • November, 1995
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