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An asymptotic expansion for the expectation of an age-dependent branching process with a submultiplicative estimate of the remainder

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

M. S. Sgibnev
M. S. Sgibnev*
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk
*
∗ Postal address: Institute of Mathematics, Novosibirsk 630090, Russia. Email address: [email protected]
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Abstract

An asymptotic expansion for the expected number, μ(t), of particles of an age-dependent branching process is obtained with a general submultiplicative estimate for the remainder term. The influence of the roots of the characteristic equation on the asymptotic behaviour of μ(t) is taken into account.

Keywords

Branching processage dependenceexpectationasymptotic behavioursubmultiplicative functionMalthusian parametercharacteristic equationLaplace transformrenewal theoremabsolutely continuous part

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K05: Renewal theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 807 - 814
Copyright
Copyright © by the Applied Probability Trust 2001 

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Footnotes

This research was supported by Grant 99-01-00504 of the Russian Foundation of Basic Research.

References

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