Geodesic
Extinction of decomposable branching processes
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 26-37

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The asymptotic behavior, as $n\rightarrow \infty $, of the conditional distribution of the number of particles in a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),\ldots,Z_{N}(m))$ with $N$ types of particles at moment $m=n-k,\, k=o(n)$, is investigated given that the extinction moment of the process equals to $n$.
Keywords: decomposable branching processes, criticality, conditional limit theorems. 
@article{DM_2015_27_4_a2,
     author = {Vladimir A. Vatutin and Elena E. Dyakonova},
     title = {Extinction of decomposable branching processes},
     journal = {Diskretnaya Matematika},
     pages = {26--37},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_4_a2/}
}
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Vladimir A. Vatutin; Elena E. Dyakonova. Extinction of decomposable branching processes. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 26-37. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a2/