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On completeness of the spectral domain of harmonizable processes
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  • Published: September 1995

On completeness of the spectral domain of harmonizable processes

  • Abol G. Miamee1 &
  • Bernd S. W. Schröder1 

Probability Theory and Related Fields volume 101, pages 303–309 (1995)Cite this article

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  • 2 Citations

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Summary

The spectral domain of harmonizable processes is studied and a criterion for its completeness is obtained. It is shown that even for periodically correlated processes the spectral domain need not be complete.

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References

  1. Chang, D.K., Rao, M.M.: In: Rao, M.M.: Bimeasures and nonstationary processes, real and stochastic analysis, pp. 7–118. New York: Wiley 1985

    Google Scholar 

  2. Cramér, H.: A contribution to the theory of stochastic processes. Proceedings 2nd Berkeley symposium on mathematics and statistics, pp. 329–339

  3. Gladyshev, E.G.: Periodically correlated processes. Soviet Math. Dokl.2, 385–388 (1961)

    Google Scholar 

  4. Hardin, J.C.: Miamee, A.G.: On a class of nonstationary stochastic processes. Indian J. Stat. (Ser. A)52, 145–156 (1990)

    Google Scholar 

  5. Hurd, H.L.: Periodically correlated processes with discontinuous correlation functions. Theory Probab. Appl.19, 834–838 (1974)

    Google Scholar 

  6. Makagon, A., Miamee, A.G.: Correlation autoregressive sequence: their representations and harmonizability, preprint (1992)

  7. Mehlman, M.: Structure and moving average representation for multidimensional strongly harmonizable processes. Stochastic Anal. Appl.9(3), 323–361 (1991)

    Google Scholar 

  8. Miamee, A.G., Salehi, H.: An example of a harmonizable process whose spectral domain is not complete. Scan. J. Stat.18, 249–254 (1991)

    Google Scholar 

  9. Niemi, H.: On orthogonally scattered dilation of bounded vector measures. Ann. Acad. Sci. Fenn. AI Math.3, 43–52 (1977)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hampton University, 23668, Hampton, VA, USA

    Abol G. Miamee & Bernd S. W. Schröder

Authors
  1. Abol G. Miamee
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  2. Bernd S. W. Schröder
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Cite this article

Miamee, A.G., Schröder, B.S.W. On completeness of the spectral domain of harmonizable processes. Probab. Th. Rel. Fields 101, 303–309 (1995). https://doi.org/10.1007/BF01200498

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  • Received: 13 October 1993

  • Revised: 08 September 1994

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01200498

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Mathematics Subject Classification

  • 28B05
  • 60G12
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