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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.