随机环境中乘积受控分枝过程矩的存在性
Existence of Moments of Multiplicative Controlled Branching Processes in a Random Environment
DOI: 10.12677/aam.2024.138386, PDF,    国家自然科学基金支持
作者: 陈祁欢*, 张 鑫：长沙理工大学数学与统计学院，湖南 长沙
关键词: 随机环境；乘积受控分枝过程；矩；Random Environment； Multiplicative Controlled Branching Process； Moments
摘要: 在深入研究经典分枝过程的基础上，进行模型的扩展与创新，进而推出随机环境中乘积受控分枝过程模型，探讨了序列 log  W n 的矩的存在性，且给出了相关证明，其中 W n = Z n / P n ， P n 为规范化序列， Z n 为随机环境中乘积受控分枝过程。
Abstract: Based on the research of classical branching processes, the model is extended and innovated, leading to a multiplicative controlled branching process in a random environment. Moreover, we explore the existence of moments of the sequence log  W n , and relevant proofs are given, where W n = Z n / P n , P n is the normalized sequence, Z n is the multiplicative controlled branching process in a random environment.
文章引用：陈祁欢, 张鑫. 随机环境中乘积受控分枝过程矩的存在性[J]. 应用数学进展, 2024, 13(8): 4049-4054. https://doi.org/10.12677/aam.2024.138386

参考文献

[1] Hambly, B. (1992) On the Limiting Distribution of a Supercritical Branching Process in a Random Environment. Journal of Applied Probability, 29, 499-518. [Google Scholar] [CrossRef] 
[2] Dion, J. and Essebbar, B. (1995) On the Statistics of Controlled Branching Processes. In: Lecture Notes in Statistics, Springer New York, 14-21. [Google Scholar] [CrossRef] 
[3] Huang, C. and Liu, Q. (2012) Moments, Moderate and Large Deviations for a Branching Process in a Random Environment. Stochastic Processes and Their Applications, 122, 522-545. [Google Scholar] [CrossRef] 
[4] Li, Y., Liu, Q. and Peng, X. (2019) Harmonic Moments, Large and Moderate Deviation Principles for Mandelbrot’s Cascade in a Random Environment. Statistics & Probability Letters, 147, 57-65. [Google Scholar] [CrossRef] 
[5] Grama, I., Liu, Q. and Miqueu, E. (2017) Berry-Esseen’s Bound and Cramér’s Large Deviation Expansion for a Supercritical Branching Process in a Random Environment. Stochastic Processes and Their Applications, 127, 1255-1281. [Google Scholar] [CrossRef] 
[6] Liu, Q. (2001) Local Dimensions of the Branching Measure on a Galton-Watson Tree. Annales de l’Institut Henri Poincare (B) Probability and Statistics, 37, 195-222. [Google Scholar] [CrossRef] 

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