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Continuous-time branching processes with decreasing state-dependent immigration

  • K. V. Mitov (a1), V. A. Vatutin (a2) and N. M. Yanev (a1)

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.

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Corresponding author

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.

References

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[21] Yosida, K. (1960) Lectures on Differential and Integral Equations. Interscience, New York.

Keywords

Continuous-time branching processes with decreasing state-dependent immigration

  • K. V. Mitov (a1), V. A. Vatutin (a2) and N. M. Yanev (a1)

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