发表机构
Nanzan University; University of Copenhagen; Vienna University（南山大学; 哥本哈根大学; 维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究尾部指数小于2的正则变化平稳序列的自正则化部分和相关比值统计量的矩存在性，发现其矩存在性与序列的极值簇相关。
AI 中文摘要
我们考虑尾部指数小于2的正则变化平稳随机变量序列(X_t)，研究这类序列的和、p型模与最大值的联合收敛性。重点关注比值统计量，包括学生化和及由对应最大值归一化的和，探究极限比值的矩存在性。我们给出极限比值具有所有矩的过程(X_t)的具体例子，但与之相反，也存在序列(X_t)使得极限比值的某些矩为无穷大，该现象源于序列中的极值簇。
英文摘要
We consider a regularly varying stationary sequence of random variables (Xt) with tail index ___ < 2. For these sequences we study the joint convergence of sums, `p- type moduli and maxima. We focus on ratio statistics, including the studentized sums and sums normalized by the corresponding maxima, and study the existence of moments for the limit ratios. We consider particular examples of processes (Xt) whose limit ratios possess all moments. But, in contrast to the latter situation, there also exist sequences (Xt) where certain moments of the limit ratio are in___nite. This phenomenon results from extremal clusters in the sequence.
Journal refStochastic Processes and their Applications, 2026, 192, pp.104810
