A continuous spectral algorithm and computer routines in the R programming environment that enable the simulation of second-order stationary and intrinsic (i.e., with second-order stationary increments or generalized increments) vector Gaussian random fields in Euclidean spaces are presented. The simulation is obtained by computing a weighted sum of cosine and sine waves, with weights that depend on the matrix-valued spectral density associated with the spatial correlation structure of the random field to simulate. The computational cost is proportional to the number of locations targeted for simulation, below that of sequential, matrix decomposition and discrete spectral algorithms. Also, the implementation is versatile, as there is no restriction on the number of vector components, workspace dimension, number and geometrical configuration of the target locations. The computer routines are illustrated with synthetic examples and statistical testing is proposed to check the normality of the distribution of the simulated random field or of its generalized increments. A by-product of this work is a spectral representation of spherical, cubic, penta, Askey, J-Bessel, Cauchy, Laguerre, hypergeometric, iterated exponential, gamma, and stable covariance models in the d -dimensional Euclidean space.

中文翻译：

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算法 1013

提出了 R 编程环境中的连续谱算法和计算机例程，能够模拟欧几里得空间中的二阶平稳和固有（即，具有二阶平稳增量或广义增量）矢量高斯随机场。该模拟是通过计算余弦波和正弦波的加权和来获得的，其权重取决于与要模拟的随机场的空间相关结构相关的矩阵值谱密度。计算成本与模拟目标位置的数量成正比，低于顺序、矩阵分解和离散谱算法。此外，实现是通用的，因为对向量组件的数量、工作空间维度没有限制，目标位置的数量和几何配置。计算机程序通过合成示例进行说明，并提出了统计测试来检查模拟随机场或其广义增量的分布的正态性。这项工作的一个副产品是在d维欧几里得空间。