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Convergence of a sequence of nearly critical branching processes with immigration


Author: Ya. M. Khusanbaev
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 201-205
MSC (2010): Primary 60J80; Secondary 62F12
DOI: https://doi.org/10.1090/tpms/960
Published electronically: August 11, 2015
MathSciNet review: 3242031
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Abstract: We study a sequence of nearly critical branching processes with immigration in the case where the rate of convergence of the expectation of the number of offsprings to 1 is slower than $ n^{-1}$. We provide sufficient conditions under which these processes converge in probability to a nonrandom process and prove a limit theorem for the fluctuations of nearly critical branching processes.


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Additional Information

Ya. M. Khusanbaev
Affiliation: Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
Email: yakubjank@mail.ru

DOI: https://doi.org/10.1090/tpms/960
Keywords: Branching process with immigration, week convergence
Received by editor(s): January 7, 2012
Published electronically: August 11, 2015
Article copyright: © Copyright 2015 American Mathematical Society