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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Aaronson, J., Gilat, D., Keane, M.S., De Valk, V.: An algebraic construction of a class of one-dependent processes. Ann. Probab. (in press)
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
Katz, M.: Rearrangements of (0–1) matrices. Israel J. Math.9, 53–72, (1971)
De Valk, V.: The maximal and minimal 2-correlation of a class of 1-dependent 0–1 valued processes. Israel J. Math. (in press)
De Valk, V.: A problem on 0–1 matrices. Compositio Mathematica (in press)
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Supported by C.N.R., Italy
Supported by Z.W.O., The Netherlands
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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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DOI: https://doi.org/10.1007/BF01794435