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.

中文翻译：

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转弯弧：一种计算有效的算法，用于模拟d球面上的各向同性矢量值高斯随机场

球体上的随机场在自然科学中起着基本作用。本文提出了一种模拟算法括号到欧氏空间中使用，用于在模拟标量或向量值的高斯随机视野的光谱转向带法d维单位球。通过Gegenbauer波的总和获得模拟的随机场，每个Gegenbauer波沿着随机定向的弧是可变的，而沿着正交于该弧的平行线是恒定的。提出了基于Berry-Esséen不等式的收敛准则，为算法的实现选择合适的参数，并通过数值实验进行了说明。这项工作的副产品是在尺寸大于或等于2的球体上与Chentsov和指数协方差模型相关的Schoenberg系数的闭式表达式。