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Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces
Journal of Theoretical Probability ( IF 0.8 ) Pub Date : 2019-05-22 , DOI: 10.1007/s10959-019-00920-1
Tianshi Lu , Chunsheng Ma

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and sufficient conditions are derived for a symmetric and continuous matrix function to be an isotropic covariance matrix function on all compact two-point homogeneous spaces. It is also shown that, for a symmetric and continuous matrix function with compact support, if it makes an isotropic covariance matrix function in the Euclidean space, then it makes an isotropic covariance matrix function on the sphere or the real projective space.

中文翻译:

紧致两点齐次空间上的各向同性协方差矩阵函数

协方差矩阵函数在本文中表征为在紧凑的两点齐次空间上平稳、各向同性和均方连续的高斯或椭圆轮廓矢量随机场。推导出对称连续矩阵函数在所有紧两点齐次空间上成为各向同性协方差矩阵函数的充要条件。还表明,对于紧支撑的对称连续矩阵函数,如果在欧几里德空间上作各向同性协方差矩阵函数,则在球面或实射影空间上作各向同性协方差矩阵函数。
更新日期:2019-05-22
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