Geodesic
On the recurrence and transience of state-dependent
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 641-660 Cet article a éte moissonné depuis la source Math-Net.Ru

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The state-dependent branching process in random environment $Z_n$—the generalization of Smith–Wilkinson's model—is considered. The Lamperti–Kersting criteria for the recurrence or transience of growth models are applied to the process $X_n:=\log Z_n$, $Z_n\ge 3$.
Keywords: branching process, random environment, state dependence, sums of independent variables, logarithmic moments. 
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S. A. Albeverio; M. V. Kozlov. On the recurrence and transience of state-dependent. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 641-660. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a0/

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