Small positive values and limit theorems for supercritical branching processes with immigration in random environment

2024/02/23 by Zhao, Yinxuan, Zhang, Mei
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2402.15279

Abstract

Let (Z_n) be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for Z are investigated. Based on these results, the central limit theorem of log Z_n and the Edgeworth expansion are obtained. The study is taken under the assumption that each individual produces 0 offspring with a positive probability.

Related

• Limit theorems for supercritical branching processes in random environment
• Small positive values for supercritical branching processes in random environment
• Subcritical branching processes in random environment with immigration: survival of a single family
• Asymptotic Behaviors for Critical Branching Processes with Immigration
• Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions