The Growth and Spread of Thegeneral Branching Random Walkj

@inproceedings{Biggins1995TheGA,
  title={The Growth and Spread of Thegeneral Branching Random Walkj},
  author={Dean Biggins},
  year={1995}
}
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; 1) 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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