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On the integral with respect to the tensor product of two random measures

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  • Boudou, Alain
  • Romain, Yves

Abstract

A Fubini-type formula for the integral with respect to the tensor product of two random measures is established in an intrinsic way. This permits one to consider a convolution product. The results are applied to a stationary continuous random function (which may be multiplicatively written with two stationary components) and to principal component analysis in the frequency domain.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:385-394
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    References listed on IDEAS

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    1. Boudou, A. & Dauxois, J., 1994. "Principal Component Analysis for a Stationary Random Function Defined on a Locally Compact Abelian Group," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 1-16, October.
    2. 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.
    3. Dehay, Dominique, 1991. "On the product of two harmonizable time series," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 347-358, August.
    4. Rosenberg, Milton, 1974. "Operators as spectral integrals of operator-valued functions from the study of multivariate stationary stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 4(2), pages 166-209, June.
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    Cited by:

    1. 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.

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