On recurrence and transience of growth models
- 1 September 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 23 (03) , 614-625
- https://doi.org/10.1017/s0021900200111787
Abstract
Let Xn be non-negative random variables, possessing the Markov property. We given criteria for deciding whether Pr(X n →∞) 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
This publication has 3 references indexed in Scilit:
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- Transience and recurrence of state-dependent branching processes with an immigration componentAdvances in Applied Probability, 1979
- Criteria for the recurrence or transience of stochastic process. IJournal of Mathematical Analysis and Applications, 1960