Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment

Afanasyev Valeriy Ivanovich ()
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Afanasyev Valeriy Ivanovich: Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkin St., Moscow, 119991, Russia

Stochastics and Quality Control, 2021, vol. 36, issue 2, 129-143

Abstract: We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time 𝑛. The offspring reproduction law in each generation is assumed to be geometric. The process is considered under the condition of its extinction after time 𝑛. Two limit theorems for this process are proved: the first one is for the time interval from 0 till 𝑛, and the second one is for the time interval from 𝑛 till + ∞ +\infty .

Keywords: Branching Process in Random Environment; Branching Process with Immigration; Limit Theorems (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/eqc-2021-0036

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