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Bellman–Harris branching processes with state-dependent immigration

Published online by Cambridge University Press:  14 July 2016

K. V. Mitov  and
N. M. Yanev
K. V. Mitov*
Affiliation:
Institute of Mathematics, Sofia
N. M. Yanev*
Affiliation:
Institute of Mathematics, Sofia
*
∗ Postal address: Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, P.O. Box 373, Bulgaria.
∗ Postal address: Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, P.O. Box 373, Bulgaria.
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Abstract

We consider critical Bellman-Harris processes which admit an immigration component only in the state 0. The asymptotic behaviour of the probability of extinction and of the first two moments is investigated and a limit theorem is also proved.

Keywords

ASYMPTOTIC BEHAVIOURPROBABILITY OF EXTINCTIONMOMENTSLIMIT DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 757 - 765
Copyright
Copyright © Applied Probability Trust 1985 

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