多径向正则变化
Multiradial Regular Variation
- University of Lausanne（洛桑大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文引入多径向正则变化，刻画随机场分量阈值以不同速率发散时的尾部行为，通过锚定质量与条件路径定律表征收敛，并证明平移不变尾部测度存在平稳实现，以移动平均为例展示尾部质量差异。
AI中文摘要：
我们引入并研究了随机场的多径向正则变化，允许分量方向的阈值以不相关的速率发散。极限测度在每个分量上是齐次的，并且在紧窗口上每个分量在绝对值上超过正水平的集合上是有限的。我们通过锚定超越质量和条件全路径定律来刻画收敛性，并在连续参数设置中结合紧窗口质量界。对于由可数离散阿贝尔群或R^m索引的场，此类中的每个平移不变尾部测度都允许严格平稳的实现。具有共享波动性的有限移动平均表明，标量行尾部测度和每个连续有限窗口上的同时超越尾部质量可以一致，而相对滞后尾部质量则不同。
英文摘要：
We introduce and study multiradial regular variation of random fields, allowing componentwise thresholds to diverge at unrelated rates. The limit measures are homogeneous in each component and finite on events where every component exceeds a positive level in absolute value somewhere on a compact window. We characterise convergence by anchor exceedance masses and conditional whole-path laws, together with a compact-window mass bound in the continuous-parameter setting. For fields indexed by a countable discrete abelian group or by R^m every shift-invariant tail measure in this class admits a strictly stationary realisation. Finite moving averages with shared volatility show that scalar row-tail measures and simultaneous-exceedance tail masses on every consecutive finite window can coincide while relative-lag tail masses differ.
