Abstract
The purpose of this note is to give a partial solution to the following problem posed by Thomas M. Cover [1]. Let (X, Y) = (Xi, Yi, i ∈ Z) be a jointly ergodic stationary stochastic process. A random process δ = (δi, i ∈ Z) is called a selection strategy if δi, ∈ {0,1} with probability one for each i, and a selection strategy δ is called sequential if for each i ≥ 1, δi is measurable with respect to $$\sigma ({{X}_{{i - 1}}},{{Y}_{{i - 1}}},{{X}_{{i - 2}}},{{Y}_{{i - 2}}}, \ldots ,{{X}_{1}},{{X}_{1}}),$$ which represents the finite past.
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