Geodesic
Properties of multitype subcritical branching processes in random environment
Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 3-23

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We study properties of a $p$-type subcritical branching process in random environment initiated at moment zero by a vector $\mathbf{z}=\left( z_{1},..,z_{p}\right) $ of particles of different types. For $p=1$ the class of processes we consider corresponds to the so-called strongly subcritical case. It is shown that the survival probability of this process up to moment $n$ behaves as $C(\mathbf{z})\lambda ^{n}$ for large $n,$ where the parameters $\lambda\in (0,1) $ and $C(z)\in (0,\infty)$ are explicitly described in terms of the characteristics of the process. We also demonstrate that the distribution of the number of particles of different types at moment $n\rightarrow \infty$ (given its survival up to this moment) does not asymptotically depend on the number and types of particles initiated the process.
Keywords: random environment, multitype branching processes, limit theorems. 
@article{DM_2020_32_3_a0,
     author = {V. A. Vatutin and E. E. D'yakonova},
     title = {Properties of multitype subcritical branching processes in random environment},
     journal = {Diskretnaya Matematika},
     pages = {3--23},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_3_a0/}
}
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V. A. Vatutin; E. E. D'yakonova. Properties of multitype subcritical branching processes in random environment. Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 3-23. http://geodesic.mathdoc.fr/item/DM_2020_32_3_a0/