论文标题
限制具有远距离依赖性的次级高斯随机场的游览集定理
Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence
论文作者
论文摘要
本文考虑了具有（可能是）无限方差的次级高斯随机场的偏差行为的渐近行为。实际上，我们考虑了此类领域的积分功能，并使用集成媒体的扩展获得了它们的限制分布。我们考虑一般的非平稳高斯随机场，包括固定和各向异性特殊情况。我们极限定理中的限制随机变量具有多个Wiener-Itô积分的形式。我们用相应的示例说明了大多数结果。
This paper considers the asymptotic behaviour of volumes of excursion sets of subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals of such fields and obtain their limiting distribution using the Hermite expansion of the integrand. We consider the general non-stationary Gaussian random fields, including stationary and anisotropic special cases. The limiting random variables in our limit theorems have the form of multiple Wiener-Itô integrals. We illustrate most results with corresponding examples.
