临界加尔顿-沃森分支过程的大偏差

Pub Date : 2024-04-19 DOI:10.1007/s10255-024-1058-y

Dou-dou Li, Wan-lin Shi, Mei Zhang

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引用次数: 0

摘要

本文考虑了临界 Galton-Watson 分支过程 {Zn}。得到了 \({S_{Z_n}}: = \sum\limits_{i = 1}^{Z_n}} {{X_i}} \) 的大偏差率，其中 {Xi, i ≥ 1} 是独立且同分布的随机变量序列，X1 位于α稳定定律的吸引域内（α∈ (0, 2)）。我们将看到，收敛速度由 X1 的尾指数和 Z1 的方差决定。我们的结果可以与超临界情况下的结果进行比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Large Deviations for a Critical Galton-Watson Branching Process

In this paper, a critical Galton-Watson branching process {Z_n} is considered. Large deviation rates of \({S_{{Z_n}}}: = \sum\limits_{i = 1}^{{Z_n}} {{X_i}} \) are obtained, where {X_i, i ≥ 1} is a sequence of independent and identically distributed random variables and X₁ is in the domain of attraction of an α-stable law with α ∈ (0, 2). One shall see that the convergence rate is determined by the tail index of X₁ and the variance of Z₁. Our results can be compared with those ones of the supercritical case.

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