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Extinction probability, regularity and asymptotic growth of Markovian populations

Published online by Cambridge University Press:  14 July 2016

Norbert Lenz
Norbert Lenz*
Affiliation:
Johannes Gutenberg-Universität
*
∗Postal address: Fachbereich Mathematik, Johannes Gutenberg-Universität in Mainz, 6500 Mainz, Postfach 3980, W. Germany.
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Abstract

The distribution of the maximum and the extinction probability for a Markovian population is derived. Asymptotic growth is described, using the sequence of sojourn times. A regularity criterion for the processes under consideration exists under certain assumptions. For a class of processes with specific population-dependent transition rates the asymptotic behaviour is given explicitly.

Keywords

MARKOVIAN POPULATIONMAXIMUM DISTRIBUTIONEXTINCTION PROBABILITYASYMPTOTIC GROWTHREGULARITYMARKOV BRANCHING PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 1 - 18
Copyright
Copyright © Applied Probability Trust 

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References

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