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Extremal two-correlations of two-valued stationary one-dependent processes
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  • Published: September 1989

Extremal two-correlations of two-valued stationary one-dependent processes

  • A. Gandolfi1,
  • M. Keane1 &
  • V. de Valk1 

Probability Theory and Related Fields volume 80, pages 475–480 (1989)Cite this article

  • 76 Accesses

  • 11 Citations

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Summary

The maximal value of the two-correlation for two-valued stationary one-dependent processes with fixed probability α of a single symbol is determined. We show that the process attaining this bound is unique except when α=1/2, when there are exactly two different processes. The analogous problem for minimal two-correlation is discussed, and partial results are obtained.

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References

  1. Aaronson, J., Gilat, D., Keane, M.S., De Valk, V.: An algebraic construction of a class of one-dependent processes. Ann. Probab. (in press)

  2. Finke, L.: Two maximization problems. A paper submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Arts, 1982

  3. Katz, M.: Rearrangements of (0–1) matrices. Israel J. Math.9, 53–72, (1971)

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  4. De Valk, V.: The maximal and minimal 2-correlation of a class of 1-dependent 0–1 valued processes. Israel J. Math. (in press)

  5. De Valk, V.: A problem on 0–1 matrices. Compositio Mathematica (in press)

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Author information

Authors and Affiliations

  1. Faculty of Technical Mathematics and Informatics, Delft University of Technology, Julianalaan 132, 2628 BL, Delft, The Netherlands

    A. Gandolfi, M. Keane & V. de Valk

Authors
  1. A. Gandolfi
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  2. M. Keane
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  3. V. de Valk
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Additional information

Supported by C.N.R., Italy

Supported by Z.W.O., The Netherlands

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Cite this article

Gandolfi, A., Keane, M. & de Valk, V. Extremal two-correlations of two-valued stationary one-dependent processes. Probab. Th. Rel. Fields 80, 475–480 (1989). https://doi.org/10.1007/BF01794435

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  • Received: 13 January 1988

  • Revised: 06 June 1988

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF01794435

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Partial Result
  • Analogous Problem
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