Comparison on the criticality parameters for two supercritical branching processes with immigration in random environments
Year: 2025
Type: article
Abstract: This paper considers two supercritical branching processes with immigration in different random environments, denoted by $\{Z_{1,n}\}$ and $\{Z_{2,m}\}$ , with criticality parameters µ 1 and µ 2 , respectively. Under certain conditions, it is known that $\frac{1}{n} \log Z_{1,n} \to \mu_1$ and $\frac{1}{m} \log Z_{2,m} \to \mu_2$ converge in probability as $m, n \to \infty$ . We present basic properties about a central limit theorem, a non-uniform Berry–Esseen’s bound, and Cramér’s moderate deviations for $\frac{1}{n} \log Z_{1,n} - \frac{1}{m} \log Z_{2,m}$ as $m, n \to \infty$ . To this end, applications to construction of confidence intervals and simulations are also given.
Authors: Yingqiu Li, Hailong Yang, Rui Li
Institution: Changsha University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Award: G7989505609
OpenAlex ID: W4414925113