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This article is cited in 2 scientific papers (total in 2 papers)
Weakly supercritical branching process in unfavourable environment
V. I. Afanasyev Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
Let $\{Z_{n}\}$ be a weakly supercritical branching process in a random environment, and $\{S_{n}\}$ be its associated random walk. We consider a natural martingale $W_{n}=Z_{n}\exp(-S_{n})$, where $n\geq 0$. We prove two limit theorems for the random process $W_{\lfloor nt\rfloor}$, where $t\in [0,1]$, which is considered either under the condition on the unfavourable environment $\{\max_{1\leq i\leq n}S_{i}\}$ or under the condition on the unfavourable environment $\{S_{n}\leq u\}$, where $u$ is some positive constant.
Keywords:
weakly supercritical branching process in a random environment, conditional functional limit theorems
Received: 27.05.2022
Citation:
V. I. Afanasyev, “Weakly supercritical branching process in unfavourable environment”, Diskr. Mat., 34:3 (2022), 3–19; Discrete Math. Appl., 34:1 (2024), 1–13
Linking options:
https://www.mathnet.ru/eng/dm1724https://doi.org/10.4213/dm1724 https://www.mathnet.ru/eng/dm/v34/i3/p3
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Abstract page: | 300 | Full-text PDF : | 39 | References: | 46 | First page: | 11 |
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