Geodesic
Reduced multitype critical branching processes in random environment
Diskretnaya Matematika, Tome 28 (2016) no. 4, pp. 58-79

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We consider a multitype critical branching process $\mathbf{Z}_{n},n=0,1,...$, in an i.i.d. random environment. Let $Z_{m,n}$ be the number of particles in this process at time $m$ having descendants at time $n$. A limit theorem is proved for the logarithm of $Z_{nt,n}$ at moments $nt,\,0\leq t\leq 1,$ conditioned on the survival of the process $\mathbf{Z}_{n}$ up to moment $n$ when $n\rightarrow \infty $.
Keywords: multitupe branching processes, reduced branching processes, random environment. 
@article{DM_2016_28_4_a5,
     author = {Elena E. D'yakonova},
     title = {Reduced multitype critical branching processes in random environment},
     journal = {Diskretnaya Matematika},
     pages = {58--79},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_4_a5/}
}
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Elena E. D'yakonova. Reduced multitype critical branching processes in random environment. Diskretnaya Matematika, Tome 28 (2016) no. 4, pp. 58-79. http://geodesic.mathdoc.fr/item/DM_2016_28_4_a5/