Statistics and Computing

, Volume 9, Issue 4, pp 265–268 | Cite as

Simulation of stationary Gaussian vector fields

  • G. Chan
  • A. T. A. Wood


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.

Circulant embedding Fast Fourier transform Toeplitz matrix 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • G. Chan
  • A. T. A. Wood

There are no affiliations available

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