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Research Article | Open Access

Self-normalized Cramér moderate deviations for a supercritical Galton-Waston process with immigration in random environments

Juan Wang( ), Wanlu Xiao
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
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Abstract

In this paper, we mainly investigated the self-normalized Cramér-type moderate deviations for the Galton-Watson process with immigration in random environments. Our central approach was to establish a self-normalized moderate deviation principle for martingales related to the Lotka-Nagaev estimator under a set of relatively broad conditions.

Keywords

Galton-Watson processimmigrationself-normalizedCramér-typemoderate deviationsrandom environment
CLC number: 60J27, 60J35

References

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AIMS Mathematics
Volume 11 Issue 2,
February 2026
Pages 4557-4570
DOI: 10.3934/math.2026183

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Cite this article:
Wang J, Xiao W. Self-normalized Cramér moderate deviations for a supercritical Galton-Waston process with immigration in random environments. AIMS Mathematics, 2026, 11(2): 4557-4570. https://doi.org/10.3934/math.2026183

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Received: 03 December 2025
Revised: 22 January 2026
Accepted: 30 January 2026
Published: 24 February 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)