论文标题
球体上各向同性高斯随机场的多级表示
Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere
论文作者
论文摘要
构建了具有独立高斯系数和局部基础函数的$ \ mathbb {s}^2 $对各向同性高斯随机字段的串联扩展。具有多级局部结构的这种表示，可以替代各向同性随机场的标准Karhunen-Loève扩展，以球形谐波为角度。通过将协方差算子的平方根应用于球形登顶，获得了基础函数。在衰减条件下，在随机场的角功率谱上显示了所得协方差依赖性多级基础的定位。此外，还给出了数值插图，并分析了球体上随机椭圆形PDE的应用。
Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to the standard Karhunen-Loève expansions of isotropic random fields in terms of spherical harmonics. The basis functions are obtained by applying the square root of the covariance operator to spherical needlets. Localization of the resulting covariance-dependent multilevel basis is shown under decay conditions on the angular power spectrum of the random field. In addition, numerical illustrations are given and an application to random elliptic PDEs on the sphere is analyzed.
