具有长程依赖的时空高斯随机场的高级移动偏移
High-level moving excursions for spatiotemporal Gaussian random fields with long range dependence
AI总结：
本文分析了含移动水平的时空Minkowski泛函等积分几何随机泛函的渐近行为，推导了时空长程依赖高斯随机场逗留测度的极限结果及一般约简原理，还研究时变阈值，结果可用于随机物理系统的统计几何分析并在宇宙学中应用。
摘要：
本文分析了一类扩展的积分几何随机泛函的渐近行为，包括移动水平下的时空Minkowski泛函。具体而言，分析中考虑了时空长程依赖（LRD）高斯随机场的逗留测度。推导的极限结果提供了空间和时间域渐近增长下的一般约简原理。还研究了时变阈值的情况。因此，所考虑的形态测度族允许对随时间显示结构变化的随机物理系统进行统计和几何分析。受宇宙学应用的启发，推导结果被应用于时空球形高斯随机场的逗留测度背景。对一些显示复杂时空依赖结构的时空高斯随机场族的结果进行了说明。
英文摘要：
The asymptotic behavior of an extended family of integral geometric random functionals, including spatiotemporal Minkowski functionals under moving levels, is analyzed in this paper. Specifically, sojourn measures of spatiotemporal long-range dependence (LRD) Gaussian random fields are considered in this analysis. The limit results derived provide general reduction principles under increasing domain asymptotics in space and time. The case of time-varying thresholds is also studied. Thus, the family of morphological measures considered allows the statistical and geometrical analysis of random physical systems displaying structural changes over time. Motivated by cosmological applications, the derived results are applied to the context of sojourn measures of spatiotemporal spherical Gaussian random fields. The results are illustrated for some families of spatiotemporal Gaussian random fields displaying complex spatiotemporal dependence structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
