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The turning arcs: a computationally efficient algorithm to simulate isotropic vector-valued Gaussian random fields on the c/-sphere

机译:转弯弧:计算C / -Sphere上的各向同性矢量值高斯随机字段的计算高效算法

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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-Esseen 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.
机译:球体上的随机字段在自然科学中发挥着基本作用。本文呈现了eUCLIDEAN空间中使用的谱转动带法的仿真算法,用于在D维单元球上模拟标量或矢量值高斯随机字段。模拟随机场通过GEGENBAUER波的总和获得,每个总体波是沿着随机定向的电弧和沿着与弧形正交的弧形恒定的恒定变量。提出了基于Berry-esseen不等式的收敛标准,为实现算法的实施方式选择合适的参数,这通过数值实验说明。该工作的副产物是与依诗ov和尺寸的球体上的依章和指数协方差模型相关联的闭合形式表达,其尺寸大于或等于2。

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