The Growth and Spread of Thegeneral Branching Random Walkj

  title={The Growth and Spread of Thegeneral Branching Random Walkj},
  author={Dean Biggins},
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. 

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 11 references

Large deviation lower bounds for general sequences of random variables

A. de Acosta, P. Ney, E. Nummelin
InRandom Walks , Brownian Motion and Interacting Particle Systemseds • 1991
View 1 Excerpt

Thevelocity of spatial population expansion

F. Metz van den Bosch, J J.A., O. Diekmann
J . Math . Biol . • 1990

General branching processes as Markov Fields

O. Nerman
Stoc . Proc . Appl . • 1989

A martingale approach to supercritical ( CMJ ) branching processes

H. Cohn
Ann . Probab . • 1985

Large deviations for a general class of random vectors

R. S. Ellis
Ann . Probab . • 1984
View 1 Excerpt

On the convergence of supercritical general ( CMJ ) branching process

R. T. Rockafellar
Z . Wahrsch . verw . Gebeite . • 1981

Spatial spread in branching processes

J. D. Biggins
Biolo - gical Growth and Spread • 1980
View 1 Excerpt

Cherno ' s Theorem in the branching randomwalk

J. D. Biggins
Jnl . Appl . Probab . • 1977

Similar Papers

Loading similar papers…