@article{Wang2026, 
author = {Juan Wang and Wanlu Xiao},
title = {Self-normalized Cramér moderate deviations for a supercritical Galton-Waston process with immigration in random environments},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4557-4570},
keywords = {Galton-Watson process, immigration, self-normalized, Cramér-type, moderate deviations, random environment},
url = {https://www.sciopen.com/article/10.3934/math.2026183},
doi = {10.3934/math.2026183},
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.}
}