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Asymptotic behaviour of Markov population processes by asymptotically linear rate of change

  • F. C. Klebaner (a1)

Abstract

Multidimensional Markov processes in continuous time with asymptotically linear mean change per unit of time are studied as randomly perturbed linear differential equations. Conditions for exponential and polynomial growth rates with stable type distribution are given. From these conditions results on branching models of populations with stabilizing reproduction for near-supercritical and near-critical cases follow.

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Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, VIC 3052, Australia.

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Research supported by the Australian Research Council grant A68930440.

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References

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