Geodesic
On the recurrence and transience of state-dependent
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 641-660

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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. 
@article{TVP_2003_48_4_a0,
     author = {S. A. Albeverio and M. V. Kozlov},
     title = {On the recurrence and transience of state-dependent},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {641--660},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a0/}
}
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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/