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On Recurrence and Transience of Growth Models
Journal of Applied Probability
Vol. 23, No. 3 (Sep., 1986), pp. 614-625
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3214001
Page Count: 12
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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.
Journal of Applied Probability © 1986 Applied Probability Trust