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Convergence of age and type distributions in multitype critical Bellman-Harris processes

Published online by Cambridge University Press:  14 July 2016

K. Rama Murthy
K. Rama Murthy*
Affiliation:
Indian Statistical Institute, Bangalore
*
∗Postal address: Indian Statistical Institute, Bangalore Centre, 31 Church St, Bangalore 560 001, India.
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Abstract

The age and type distributions (conditioned on non-extinction) in a critical Bellman-Harris process are shown to converge in probability to a deterministic distribution under a finite first-moment hypothesis on the offspring distribution and a tightness condition on the lifetime distributions.

Keywords

BELLMAN–HARRIS PROCESSCRITICALEXTINCTION PROBABILITIESAGE AND TYPE DISTRIBUTIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 948 - 955
Copyright
Copyright © Applied Probability Trust 

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References

Athreya, K. B. and Kaplan, N. (1978) The additive property and its applications in branching processes. In Advances in Probability, Vol. 5, ed. Joffe, A. and Ney, P. E., Dekker, New York.Google Scholar
Kaplan, N. and Asmussen, S. (1976) Branching random walks II. Stoch. Proc. Appl. 4, 15–32.CrossRefGoogle Scholar
Seneta, E. (1973) Non-Negative Matrices. Allen and Unwin, London.Google Scholar