Simulation of stationary Gaussian vector fields

被引:49
作者
Chan, G
Wood, ATA
机构
[1] Univ New S Wales, Sch Math, Dept Stat, Sydney, NSW 2052, Australia
[2] Univ Bath, Sch Math Sci, Bath BA2 7AY, Avon, England
关键词
circulant embedding; Fast Fourier Transform; Toeplitz matrix;
D O I
10.1023/A:1008903804954
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In earlier work we described a circulant embedding approach for simulating scalar-valued stationary Gaussian random fields on a finite rectangular grid, with the covariance function prescribed. Here, we explain how the circulant embedding approach can be used to simulate Gaussian vector fields. As in the scalar case, the simulation procedure is theoretically exact if a certain non-negativity condition is satisfied. In the vector setting, this exactness condition takes the form of a nonnegative definiteness condition on a certain set of Hermitian matrices. The main computational tool used is the Fast Fourier Transform. Consequently, when implemented appropriately, the procedure is highly efficient, in terms of both CPU time and storage.
引用
收藏
页码:265 / 268
页数:4
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