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On spectral and random measures associated to discrete and continuous-time processes

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  • Boudou, Alain
  • Romain, Yves

Abstract

In this paper, results for the tensor product of discrete and continuous-time processes are presented. They concern the definition and the study of the properties of the processes associated to the (tensor and convolution) products of two (spectral and random) measures. An example for the product of scalar and vector-valued stationary processes is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:2:p:145-157
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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. Romain, Yves, 2002. "Perturbation of functional tensors with applications to covariance operators," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 253-264, July.
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    Citations

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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.
    2. Boudou, Alain & Viguier-Pla, Sylvie, 2022. "Principal components analysis and cyclostationarity," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Boudou, A. & Cabral, E.N. & Romain, Y., 2010. "Centered and non-centered principal component analyses in the frequency domain," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 96-103, January.
    4. 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.
    5. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    6. Boudou, Alain & Viguier-Pla, Sylvie, 2010. "Relation between unit operators proximity and their associated spectral measures," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1724-1732, December.
    7. Boudou, Alain & Viguier-Pla, Sylvie, 2019. "Commuter of operators in a Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 244-262.
    8. Boudou, Alain & Viguier-Pla, Sylvie, 2016. "Gap between orthogonal projectors—Application to stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 282-300.

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