Geodesic
Multitype branching processes in random environment: survival probability for the critical case
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 634-653

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We investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in an environment generated by a sequence of independent identically distributed random variables. Under fairly general assumptions on the form of the offspring generating functions of particles, we show that the probability of survival up to generation $n$ of the process initiated at moment zero by a single particle of type $i$ is equivalent to $\beta_in^{-1/2}$, where $\beta_i$ is a positive constant. This assertion essentially generalizes a number of previously known results.
Keywords: branching processes, random environment, survival probability, change of measure. 
@article{TVP_2017_62_4_a0,
     author = {V. A. Vatutin and E. E. D'yakonova},
     title = {Multitype branching processes in random environment: survival probability for the critical case},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {634--653},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a0/}
}
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V. A. Vatutin; E. E. D'yakonova. Multitype branching processes in random environment: survival probability for the critical case. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 634-653. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a0/