期刊论文

Li, Yingqiu

英文

Communications in Statistics - Theory and Methods

0361-0926

2022

51

3

826-839

10.1080/03610926.2020.1756330

This work was supported by the National Natural Science Foundation of China (Grant No. 11571052, 11731012), the Hunan Provincial Natural Science Foundation of China (Grant No. 2018JJ2417), and the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Grant No. 2018MMAEZD02). The authors are grateful to anonymous referees and Professor Quansheng Liu for their very valuable comments and remarks, which significantly contributed to improving the quality of the paper.

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Let (Formula presented.) be a supercritical branching process with immigration (Formula presented.) in a random environment ξ. We are interested in the almost sure (a.s.) convergence rate of the submartingale (Formula presented.) to its limit (Formula presented.) where (Formula presented.) is an usually used norming sequence. The result about convergence a.s. are as following. Under a moment condition of order (Formula presented.) and (Formula presented.) where, (Formula presented.) (Formula presented.) a.s. for some a > 0 that we find explici...