Extremal two-correlations of two-valued stationary one-dependent processes. (English) Zbl 0638.60056
The maximal value of the two-correlation for two-valued stationary one- dependent processes with fixed probability \(\alpha\) of a single symbol is determined. We show that the process attaining this bound is unique except when \(\alpha =\), when there are exactly two different processes. The analogous problem for minimal two-correlation is discussed, and partial results are obtained.
MSC:
| 60G10 | Stationary stochastic processes |
| 28D05 | Measure-preserving transformations |
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
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) · Zbl 0681.60038 |
| [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) · Zbl 0215.33405 · doi:10.1007/BF02771620 |
| [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) · Zbl 0712.60040 |
| [5] | De Valk, V.: A problem on 0–1 matrices. Compositio Mathematica (in press) · Zbl 0741.15007 |
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