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Continuous-time branching processes with decreasing state-dependent immigration

Published online by Cambridge University Press:  01 July 2016

K. V. Mitov ,
V. A. Vatutin  and
N. M. Yanev
K. V. Mitov*
Affiliation:
Institute of Mathematics, Sofia
V. A. Vatutin*
Affiliation:
Steklov Mathematical Institute, Moscow
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: Steklov Mathematical Institute, Academy of Sciences of the USSR, 117969 Moscow, 42 Vavilov St, USSR.
∗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

This paper deals with continuous-time branching processes which allow a temporally-decreasing immigration whenever the population size is 0. In the critical case the asymptotic behaviour of the probability of non-extinction and of the first two moments is investigated and different types of limit theorems are also proved.

Keywords

ASYMPTOTIC BEHAVIOURPROBABILITY OF NON-EXTINCTIONMOMENTSLIMIT DISTRIBUTIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 697 - 714
Copyright
Copyright © Applied Probability Trust 1984 

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