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The first- and last-birth problems for a multitype age-dependent branching process

  • J. D. Biggins (a1)
Abstract

If Bn is the time of the first birth in the nth generation in a supercritical irreducible multitype Crump–Mode process then when there are people in every generation Bn/n converges to a constant; if Dn is the time of the last birth in the nth generation then Dn/n also converges to a constant on the survival set. Analogous results hold for the extreme members of the nth generation in a branching random walk.

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References
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Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.
Kingman, J. F. C. (1975) The first birth problem for an age-dependent branching process. Ann. Prob. 3, 790801.
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Mode, C. J. (1971) Multitype Branching Processes, Elsevier, New York.
Ney, P. E. (1964) Generalized branching processes 1: Existence and uniqueness theorems. Illinois J. Math. 8, 316331.
Pyke, R. and Schaufele, R. (1966) Limit theorems for Markov renewal processes. Ann. Math. Statist. 35, 17461764.
Seneta, E. (1973) Non-Negative Matrices. Allen and Unwin, London.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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