随机环境加权分枝过程的方差和Fuk-Nagaev型不等式
The Variance and Fuk-Nagaev Type Inequality for Weighted Branching Processes in a Random Environment
DOI: 10.12677/AAM.2023.1210411, PDF,  被引量    国家自然科学基金支持
作者: 邓 琳*, 陈祁欢, 鲁 展：长沙理工大学数学与统计学院，湖南 长沙
关键词: 随机环境；加权分枝过程；方差；Fuk-Nagaev型不等式；Random Environment； Weighted Branching Process； Variance； Fuk-Nagaev Type Inequality
摘要: 在对随机环境中加权分枝过程(Yn)的研究基础上，考虑其规范化过程Wn的方差及其收敛性，并予以了详细的证明，其中规范化过程为，是规范化序列，是随机环境分枝过程相关结论的拓展；并且建立了一个关于统计量的Fuk-Nagaev型不等式。
Abstract: On the basis of the research on the weighted branching process (Yn) in random environments, the variance and convergence of its normalization process Wn are considered, and the de-tailed proof is provided. The normalization process is , and is the normalized se-quence, which is an extension of the conclusions related to the branching process in random envi-ronments. Besides, we establish a Fuk-Nagaev type inequality for .
文章引用：邓琳, 陈祁欢, 鲁展. 随机环境加权分枝过程的方差和Fuk-Nagaev型不等式[J]. 应用数学进展, 2023, 12(10): 4183-4188. https://doi.org/10.12677/AAM.2023.1210411

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