论文标题
转向弧：一种计算高效算法，用于模拟$ d $ - sphere上的各向同性矢量值高斯随机字段
The Turning Arcs: a Computationally Efficient Algorithm to Simulate Isotropic Vector-Valued Gaussian Random Fields on the $d$-Sphere
论文作者
论文摘要
球体上的随机场在自然科学中起着基本作用。本文为欧几里得空间中使用的频谱转谱带方法提供了模拟算法括号，用于模拟$ d $尺寸单位球体上的标量或矢量值的高斯随机字段。模拟的随机场是通过gegenbauer波的总和获得的，gegenbauer波的总和沿随机取向的弧线可变，并且沿着与ARC的平行线正交沿恒定恒定。提出了基于浆果 - 埃塞恩不平等的收敛标准，以选择用于实现算法的合适参数，该参数通过数值实验进行了说明。这项工作的副产品是与尺寸大于或等于2的球体上与Chentsov和指数协方差模型相关的Schoenberg系数的封闭式表达。
Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued Gaussian random fields on the $d$-dimensional unit sphere. The simulated random field is obtained by a sum of Gegenbauer waves, each of which is variable along a randomly oriented arc and constant along the parallels orthogonal to the arc. Convergence criteria based on the Berry-Esséen inequality are proposed to choose suitable parameters for the implementation of the algorithm, which is illustrated through numerical experiments. A by-product of this work is a closed-form expression of the Schoenberg coefficients associated with the Chentsov and exponential covariance models on spheres of dimensions greater than or equal to 2.
