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Structure of the random measure associated with an isotropic stationary process

Author

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  • Alain, Boudou
  • Sylvie, Viguier-Pla

Abstract

Each stationary process can be biunivoquely associated with a random measure, through the Fourier transform. Consequently, every particularity of a process in the temporal domain has its corresponding one in the frequency domain. We propose to study the characteristics of the random measure when the process is isotropic. For that purpose, we will define the tensor product of random measures. A simulated example will illustrate such processes.

Suggested Citation

  • Alain, Boudou & Sylvie, Viguier-Pla, 2014. "Structure of the random measure associated with an isotropic stationary process," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 111-128.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:111-128
    DOI: 10.1016/j.jmva.2013.08.001
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    References listed on IDEAS

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    1. Boudou, Alain & Romain, Yves, 2002. "On spectral and random measures associated to discrete and continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 145-157, September.
    2. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    3. Boudou, Alain & Romain, Yves, 2010. "On the integral with respect to the tensor product of two random measures," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 385-394, February.
    4. Crujeiras, Rosa M. & Fernández-Casal, Rubén & González-Manteiga, Wenceslao, 2008. "An L2 -test for comparing spatial spectral densities," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2543-2551, October.
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