Convergence of a sequence of nearly critical branching processes with immigration

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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Identifiers

DOI

10.1090/tpms/960

Citations and references