On recurrence and transience of growth models

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.