Abstract:
The almost critical branching processes $Z_{k,n}$ in a random environment is considered. It was shown that the survival probabilities for the processes $Z_{n,n}$ and $Z_n$ are equivalent under rather natural assumptions on the closeness of $Z_{k,n}$ and $Z_k$. This paper contains examples of applications of this result and justifies the need for imposed conditions.
Keywords:random walks, branching processes, random environments.
The work was supported by the Russian Science Foundation under grant no. 24-11-00037, https://rscf.ru/en/project/24-11-00037/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences.
Received: 30.07.2024
Document Type:
Article
UDC:519.218.27
Language: Russian
Citation:
V. V. Kharlamov, “Asymptotic behavior of the survival probability of almost critical branching processes in a random environment: models and examples”, Diskr. Mat., 36:4 (2024), 138–157
\Bibitem{Kha24}
\by V.~V.~Kharlamov
\paper Asymptotic behavior of the survival probability of almost critical branching processes in a random environment: models and examples
\jour Diskr. Mat.
\yr 2024
\vol 36
\issue 4
\pages 138--157
\mathnet{http://mi.mathnet.ru/dm1843}
\crossref{https://doi.org/10.4213/dm1843}
Citation in format AMSBIB
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