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.

中文翻译：

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具有长程相关性的从属高斯随机场偏移集的极限定理

本文考虑了具有（可能）无限方差的从属高斯随机场的偏移集体积的渐近行为。实际上，我们考虑这些场的积分泛函并使用被积函数的 Hermite 展开来获得它们的极限分布。我们考虑一般的非平稳高斯随机场，包括平稳和各向异性的特殊情况。我们极限定理中的极限随机变量具有多重 Wiener-Itô 积分的形式。我们用相应的例子来说明大多数结果。