Geodesic
Galton--Watson branching processes in a random environment.~II: Finite-dimensional distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 231-268

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Let $Z_n$ be the number of particles at moment $n$ in a branching process in a random environment. Assuming that $Z_n$ is “critical” in a certain sense we prove theorems describing the asymptotic behavior as $n\to\infty$ of the distribution of the vector $(Z_{[nt_1]},\dots,Z_{[nt_{b}]})$, of the number of particles in the process at moments $0[nt_1]\dots[nt_{b}]=n$ given $ Z_n>0$.
Keywords: branching processes in random environment, survival probability, limit theorems, critical branching process, random walks, Spitzer condition
Mots-clés : stable distributions, joint distributions. 
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     author = {V. A. Vatutin and E. E. D'yakonova},
     title = {Galton--Watson branching processes in a random {environment.~II:} {Finite-dimensional} distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {231--268},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a1/}
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V. A. Vatutin; E. E. D'yakonova. Galton--Watson branching processes in a random environment.~II: Finite-dimensional distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 231-268. http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a1/