论文标题
各向同性希尔伯特价值的球形随机场的渐近学
Asymptotics for isotropic Hilbert-valued spherical random fields
论文作者
论文摘要
在本文中，我们介绍了各向同性希尔伯特值的球体随机场的概念，从而将各向同性球体随机场的概念扩展到无限二维设置。然后，我们建立一个频谱表示定理和功能性Schoenberg定理。遵循针对实际情况的一些关键结果，我们证明了高频制度中样品功率谱运算符的一致性和定量中心限制定理。
In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg's theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.
