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Relation between unit operators proximity and their associated spectral measures

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  • Boudou, Alain
  • Viguier-Pla, Sylvie

Abstract

In this paper, we study how the local concentration of the spectral measure can be expressed in the temporal domain for stationary processes. For this purpose, we establish an equivalence between the proximity of the shift operators (which are unit operators) and the associated projector valued spectral measures. An illustration is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1724-1732
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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. anonymous, 1991. "Fed upgrades functional cost analysis program," Financial Update, Federal Reserve Bank of Atlanta, issue Win, pages 1-2,6.
    3. Dominique Dehay & Vincent Monsan, 2007. "Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 223-253, October.
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    Cited by:

    1. 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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