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Bellman-Harris branching processes with a special type of state-dependent immigration

Published online by Cambridge University Press:  01 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 for both authors: Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev str., 1113 Sofia, Bulgaria.
Postal address for both authors: Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev str., 1113 Sofia, Bulgaria.
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Abstract

We investigate critical Bellman-Harris processes which allow immigration of new particles whenever the population size is 0. Under some special conditions on the immigration component the asymptotic behaviour of the probability of extinction is obtained and limit theorems are also proved.

Keywords

PROBABILITY OF EXTINCTIONLIMIT DISTRIBUTIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 270 - 283
Copyright
Copyright © Applied Probability Trust 1989 

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