论文标题
涉及高血压的广义产品空间上的多元高斯随机场
Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus
论文作者
论文摘要
该论文处理在涉及高血压的通用产品空间上定义的多元高斯随机场。高斯性的假设意味着有限尺寸分布将完全由协方差函数指定，在这种情况下为矩阵质量映射。我们首先考虑光谱表示，而光谱表示又允许表征这种协方差函数。然后，我们提供一些构建这些矩阵有价值映射的方法。最后，我们考虑逃避径向对称性的策略（在空间统计中称为各向异性），并为这种更一般的情况提供表示定理。
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the covariance functions, being in this case matrix valued mappings. We start by considering the spectral representations that in turn allow for a characterization of such covariance functions. We then provide some methods for the construction of these matrix valued mappings. Finally, we consider strategies to evade radial symmetry (called isotropy in spatial statistics) and provide representation theorems for such a more general case.
