Limit properties for branching process affected by communicable diseases in random environments

• Published in: Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 49; no. 1; pp. 53 - 59
• Main Author: Ren, Min
• Format: Journal Article
• Language: Chinese
• Published: Hangzhou Zhejiang University 01.01.2022; Zhejiang University Press
• Subjects: Convergence; Random variables; 传染性疾病; 几乎处处收敛; 分枝过程; 随机环境
• ISSN: 1008-9497
• DOI: 10.3785/j.issn.1008-9497.2022.01.008

The model of branching process {Zn,n∈N} affected by communicable diseases in independent random environment is proposed,and the limit properties of this model are discussed.Under the normalization factors {Sn,n∈N} and {Un,n∈N},the normalization processes {W?n,n∈N} and {Wˉn,n∈N} are studied,the sufficient conditions of {W?n,n∈N} and {Wˉn,n∈N} a.s.and L1 convergence are given; the sufficient condition of {W?n,n∈N}L2 convergence,a sufficient condition and a necessary condition for the limit of {W?n,n∈N} converging to a non-degenerate at 0 random variable are obtained.