Geodesic
On functional limit theorems for branching processes with dependent immigration
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 755-772

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In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deter-ministic function under assumptions that immigration satisfies some mixing conditions, the offspring mean tends to its critical value 1 and immigration mean and variance controlled by regularly varying functions. Moreover, we obtain a fluctuation limit theorem for branching process with immig-ration when immigration generated by a sequence of $m$-dependent random variables. In this case the limiting process is a time-changed Wiener process. Our results extend the previous known results in the literature.
Keywords: Branching process, regularly varying functions, $m$-dependence, $\rho$-mixing, functional limit theorems.
Mots-clés : immigration 
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     author = {S. O. Sharipov},
     title = {On functional limit theorems for branching processes with dependent immigration},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {755--772},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a26/}
}
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S. O. Sharipov. On functional limit theorems for branching processes with dependent immigration. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 755-772. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a26/