Geodesic
The limit theorems for branching processes with immigration
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 766-773 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider branching processes (discrete time) with $n$ types of particles and immigration of particles from «external environment». The evolution of the last is described by some finite Markov chain. We prove limit theorems for critical and subcritical cases. 
@article{TVP_1977_22_4_a7,
     author = {A. K. Polin},
     title = {The limit theorems for branching processes with immigration},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {766--773},
     year = {1977},
     volume = {22},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a7/}
}
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A. K. Polin. The limit theorems for branching processes with immigration. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 766-773. http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a7/