我们能否进一步改进平稳ρ-混合序列的中心极限定理？
Can we further improve the central limit theorem for stationary $ρ$-mixing sequences $?$
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中文总结 AI 辅助
该研究针对平稳ρ-混合序列的中心极限定理，在现有条件接近必要的基础上，提出迭代块大小技术改进不可和系数情形的条件，填补边界空白并论证准则尖锐性。
中文摘要 AI 辅助
通过Peligrad和Bradley的开创性工作，ρ-混合序列中心极限定理的现有充分条件已被证明非常接近必要条件。然而，我们证明当ρ-混合系数不可和时，这些条件仍可进一步改进，填补了边界情形的长期空白。核心思想是一种迭代块大小技术，可实现对慢变方差分量的精确评估。最后，研究了已知例子和新的推广（包括迭代对数混合率）以论证我们准则的尖锐性，揭示了清晰的参数结构并提出了相关开放问题。
英文摘要
Through the seminal works of Peligrad and Bradley, the existing sufficient conditions for the central limit theorem for $ρ$-mixing sequences are known to be very close to necessary. Nevertheless, we show that further improvements to these conditions are achievable when the $ρ$-mixing coefficients are non-summable, bridging a long-standing gap in the borderline case. The key idea is an iterative block-size technique that enables precise evaluations of the slowly varying variance components. Finally, known examples and new extensions--including iterated logarithmic mixing rates--are investigated to demonstrate the sharpness of our criteria, revealing a clear parameter structure and posing related open problems.
发表机构
- Graduate School of Economics, The university of Osaka（大阪大学经济学研究科）
机构由 AI 辅助整理，请以论文原文为准。
