Geodesic
On asymptotics of branching processes with immigration
Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 113-122.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a sequence of almost critical branching processes with immigration supposing that the immigration process is weakly stationary. The rate of growth and asymptotic properties of fluctuations of such branching processes are investigated.
Keywords: branching processes, immigration, stationary process. 
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Ya. M. Khusanbaev. On asymptotics of branching processes with immigration. Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 113-122. http://geodesic.mathdoc.fr/item/DM_2016_28_1_a6/

[1] Athreya K.B., Ney P.E., Branching Processes, Springer-Verlag, New York, 1972, 288 pp. | MR | Zbl

[2] Seneta E., “An explicit-limit theorem for the critical Galton-Watson process with Immigration”, J. Roy. Stat. Soc., 32 (1970), 149–152 | MR | Zbl

[3] Wei C.Z., Winicki J.,, “Some asymptotic results for the branching process with immigration”, Stoch. Process. Appl., 31 (1989), 261–282 | DOI | MR | Zbl

[4] Rakhimov I., “Functional limit theorems for critical processes with immigration”, Adv. Appl. Probab., 39 (2007), 1054–1069 | DOI | MR

[5] | MR | Zbl

[6] Nagaev S. V., “A limit theorem for branching processes with immigration”, Theory Probab. Appl., 20:1 (1975), 176–179 | DOI | MR | Zbl

[7] Sriram T.N., “Invalidity of bootstrap for critical branching process with immigration”, Ann. Statist., 22 (1994), 1013–1023 | DOI | MR | Zbl

[8] Ispany M., Pap G. and Van Zuijlen M.C.A., “Fluctuation limit of branching processes with immigration and estimation of the mean”, Adv. Appl. Probab., 37 (2005), 523–528 | DOI | MR

[9] Khusanbaev Ya. M., “Almost critical branching processes and limit theorems”, Ukr. Math. J., 61:1 (2009), 154–163 | DOI | MR | Zbl

[10] Billingsli P., Skhodimost veroyatnostnykh mer, M.: Nauka, 1977, 352 pp. | MR

[11] Shiryaev A. N., “Probability”, Graduate Texts in Mathematics, 95, 2, Springer-Verlag, New York, 1996, 624 pp. | DOI | MR | MR

[12] Sirazhdinov S.Kh., Formanov Sh.K., Predelnye teoremy dlya summ sluchainykh vektorov, svyazannykh v tsep Markova, Tashkent: Fan, 1979, 171 pp. | MR

[13] Khusanbaev Ya. M., “On the convergence rate in one limit theorem for branching processes with immigration”, Siberian Math. J., 55:1 (2014), 178–184 | DOI | MR | Zbl

[14] Asadullin M. Kh., Nagaev S. V., “Limit theorems for a critical branching process with immigration”, Math. Notes, 32:4 (1982), 750–757 | DOI | MR | Zbl

[15] Badalbaev I. S., Zubkov A. M., “Limit theorems for a sequence of branching processes with immigration”, Theory Probab. Appl., 28:2 (1984), 404–409 | DOI | MR | Zbl | Zbl