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The maximal and minimal 2-correlation of a class of 1-dependent 0-1 valued processes. (English) Zbl 0712.60040
The maximal and minimal value of \(P[X_ N=X_{N+1}=1]\) is computed for fixed \(P[X_ N=1]\), where \((X_ N)_{N\in {\mathbb{Z}}}\) is a 0-1 valued one-dependent process obtained by a coding (actually a two-block-factor) of an i.i.d. sequence of uniformly distributed random variables with a subset of the unit square.
The discrete version of this problem is solved by the author [Compos. Math. 71, No.2, 139-179 (1989)].
Reviewer: V.de Valk

MSC:
60G10 Stationary stochastic processes
28D05 Measure-preserving transformations
26D15 Inequalities for sums, series and integrals
28A75 Length, area, volume, other geometric measure theory
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