Geodesic
On a decomposable branching process with two types of particles
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 7-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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A decomposable Galton–Watson branching process with two types of particles is considered. It is assumed that particles of the first type produce particles of both the first and the second types, and produce them in equal amounts, while particles of the second type only produce particles of the same type. An asymptotic formula is obtained for the probability that the total number of particles of the second type up to time $N$ is greater than $\theta N$, where $\theta$ is a positive constant and $N\to\infty$. A limit theorem is established for the total number of particles of the first type considered under the condition that the total number of particles of the second type up to time $N$ is greater than $\theta N$. 
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     author = {V. I. Afanasyev},
     title = {On a~decomposable branching process with two types of particles},
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     url = {http://geodesic.mathdoc.fr/item/TM_2016_294_a0/}
}
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V. I. Afanasyev. On a decomposable branching process with two types of particles. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 7-19. http://geodesic.mathdoc.fr/item/TM_2016_294_a0/

[1] Vatutin V. A., Dyakonova E. E., “Razlozhimye vetvyaschiesya protsessy s fiksirovannym momentom vyrozhdeniya”, Tr. MIAN, 290, 2015, 114–135 | MR | Zbl

[2] Vatutin V. A., Dyakonova E. E., “O vyrozhdenii razlozhimykh vetvyaschikhsya protsessov”, Diskret. matematika, 27:4 (2015), 26–37 | DOI

[3] Afanasev V. I., “Funktsionalnye predelnye teoremy dlya razlozhimogo vetvyaschegosya protsessa s dvumya tipami chastits”, Diskret. matematika, 27:2 (2015), 22–44 | DOI | MR

[4] Lindvall T., “Convergence of critical Galton–Watson branching processes”, J. Appl. Probab., 9:2 (1972), 445–450 | DOI | MR | Zbl

[5] Lindvall T., “Limit theorems for some functionals of certain Galton–Watson branching processes”, Adv. Appl. Probab., 6:2 (1974), 309–321 | DOI | MR | Zbl

[6] Kolchin V. F., Sluchainye otobrazheniya, Nauka, M., 1984 | MR