Limit Theorems for a Supercritical Branching Process with Immigration at Zero in a Random Environment
Doudou Li, Mei Zhang, Yinxuan Zhao
2023, v.29, Issue 5, 661-681
ABSTRACT
Let Z be a supercritical branching process with immigration at zero
in a random environment, where the immigration is allowed entering a generation
i the previous generation is empty. The limit theorems for the naturally
normalized population size Wn shall be investigated, under both the annealed
law and quenched law. In addition, in the linear fractional case, the harmonic
moments of W and the convergence rate of the transition probabilities p(n)
l;j of
Z are studied.
doi:10.61102/1024-2953-mprf.2023.29.5.003
Keywords: branching process, immigration, random environment, state dependent, supercritical, linear fractional
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