Theory of Probability and Mathematical Statistics
Convergence of a sequence of nearly critical branching processes with immigration
Ya. M. Khusanbaev
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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.
Keywords: Branching process with immigration, week convergence
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