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Covariance Models and Simulation Algorithm for Stationary Vector Random Fields on Spheres Crossed with Euclidean Spaces
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2021-09-13 , DOI: 10.1137/20m1372020
Xavier Emery , Alfredo Alegría , Daisy Arroyo

SIAM Journal on Scientific Computing, Volume 43, Issue 5, Page A3114-A3134, January 2021.
This paper focuses on vector random fields defined on $\mathbb{S}^d\times \mathbb{R}^k$, $d \geq 2$ and $k \geq 1$, with covariance functions that depend on the geodesic distance in $\mathbb{S}^d$ and on the separation vector in $\mathbb{R}^k$. First, we propose parametric families of nonseparable covariance functions with closed-form expressions and explicit spectral representations. Then, we derive an algorithm for fast simulation of such random fields, which combines spectral simulation methods in $\mathbb{S}^d$ and $\mathbb{R}^k$ previously introduced in the literature and relies on importance sampling techniques. We provide computer codes and practical guidelines and describe the advantages of our proposal in comparison to other methods.


中文翻译:

与欧几里德空间相交的球面上的平稳向量随机场的协方差模型和仿真算法

SIAM 科学计算杂志,第 43 卷,第 5 期,第 A3114-A3134 页,2021 年 1 月。
这篇论文的重点是定义在 $\mathbb{S}^d\times \mathbb{R}^k$, $d \geq 2$ 和 $k \geq 1$ 上的向量随机场,协方差函数依赖于测地线$\mathbb{S}^d$ 中的距离和 $\mathbb{R}^k$ 中的分离向量。首先,我们提出了具有封闭形式表达式和显式谱表示的不可分离协方差函数的参数族。然后,我们推导出了一种快速模拟此类随机场的算法,该算法结合了之前在文献中介绍的 $\mathbb{S}^d$ 和 $\mathbb{R}^k$ 中的谱模拟方法,并依赖于重要性采样技术. 我们提供计算机代码和实用指南,并描述我们的建议与其他方法相比的优势。
更新日期:2021-09-14
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