Abstract:
The research focuses on lower large deviation probabilities for branching process in independent identically distributed random environment. Under some moment assumptions and the left-hand Cramer condition we show that the lower large deviation probabilities have the same asymptotics (due to a constant multiplier) as the corresponding probability for the associated random walk. We consider only the first deviation zone.
Keywords:
branching processes, random environment, lower large deviations, Cramer condition.
The work was supported by the Russian Science Foundation under grant no. 4-11-00037, https://rscf.ru/en/project/24-11-00037/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences.
Received: 18.06.2024
Document Type:
Article
UDC:519.218.27
Language: Russian
Citation:
A. V. Shklyaev, “Lower large deviations for a branching process in a random environment”, Diskr. Mat., 36:3 (2024), 127–140
\Bibitem{Shk24}
\by A.~V.~Shklyaev
\paper Lower large deviations for a branching process in a random environment
\jour Diskr. Mat.
\yr 2024
\vol 36
\issue 3
\pages 127--140
\mathnet{http://mi.mathnet.ru/dm1831}
\crossref{https://doi.org/10.4213/dm1831}