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

Juan Wang; Wanlu Xiao; Juan Wang; Wanlu Xiao

doi:10.3934/math.2026183

AIMS Mathematics

2026, Volume 11, Issue 2: 4557-4570. doi: 10.3934/math.2026183

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Research article

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

Received: 03 December 2025 Revised: 22 January 2026 Accepted: 30 January 2026 Published: 24 February 2026
MSC : 60J27, 60J35

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.
- Galton-Watson process,
- immigration,
- self-normalized,
- Cramér-type,
- moderate deviations,
- random environment
Citation: Juan Wang, Wanlu Xiao. Self-normalized Cramér moderate deviations for a supercritical Galton-Waston process with immigration in random environments[J]. AIMS Mathematics, 2026, 11(2): 4557-4570. doi: 10.3934/math.2026183

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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.

References

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