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On Recurrence and Transience of Growth Models

G. Kersting
Journal of Applied Probability
Vol. 23, No. 3 (Sep., 1986), pp. 614-625
DOI: 10.2307/3214001
Stable URL: http://www.jstor.org/stable/3214001
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Recurrence and Transience of Growth Models
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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(Xn+1 2 ∣ Xn = x) for large x. The assumptions are chosen such that for example population-dependent branching processes can be treated by our results.

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