Geodesic
Limit theorem for stationary distribution of a critical controlled branching process with immigration
Diskretnaya Matematika, Tome 35 (2023) no. 3, pp. 5-19

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We consider the sequence $\{{\xi_{n,t}}\}_{t\geq1} $ of controlled critical branching processes with immigration, where $n=1,2,\ldots$ is an integer parameter limiting the population size. It is shown that for $n\rightarrow\infty $ the stationary distributions of considered branching processes normalized by $\sqrt{n}$ converge to the distribution of a random variable whose square has a gamma distribution.
Keywords: controlled branching processes, Markov chain, stationary distribution, limit theorem, gamma distribution, the method of moments } In conclusion, the author expresses his sincere gratitude to A.M. Zubkov for his attention to the work and valuable comments. \begin{thebibliography}{99. 
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     author = {V. I. Vinokurov},
     title = {Limit theorem for stationary distribution of a critical controlled branching process with immigration},
     journal = {Diskretnaya Matematika},
     pages = {5--19},
     publisher = {mathdoc},
     volume = {35},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2023_35_3_a1/}
}
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V. I. Vinokurov. Limit theorem for stationary distribution of a critical controlled branching process with immigration. Diskretnaya Matematika, Tome 35 (2023) no. 3, pp. 5-19. http://geodesic.mathdoc.fr/item/DM_2023_35_3_a1/