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On recurrence and transience of growth models

Published online by Cambridge University Press:  14 July 2016

G. Kersting
G. Kersting*
Affiliation:
J. W. Goethe-Universität, Frankfurt
*
∗ Postal address: Fachbereich Mathematik, J. W. Goethe-Universität, D-6000 Frankfurt, W. Germany.
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Abstract

Let Xn be non-negative random variables, possessing the Markov property. We given criteria for deciding whether Pr(Xn →∞) is positive or 0. It turns out that essentially this depends on the magnitude of E(Xn +1 | Xn = x) compared to that of E(X 2 n+1 | Xn = x) for large x. The assumptions are chosen such that for example population-dependent branching processes can be treated by our results.

Keywords

LYAPUNOV FUNCTIONMARTINGALESMARKOV PROPERTYSTATE-DEPENDENT BRANCHING PROCESS

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 614 - 625
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research partially supported by the SFB 123, ‘Stochastische Mathematische Modelle', Heidelberg.

References

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