This paper is concerned with the following mathematical problem. Let X denote a stationary time-discrete random process whose variables, …, X−1, X0, X1, …, take values from the finite set of real numbers {x1, x2, …, xk}. Let X have mean zero and a given covariance sequence pk= EXiXi+k, j, k = 0, ±1, ±2, …. What is the largest entropy that X can have and what is the probability structure of this most random process of given second moments?
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D. Slepian (1972) studied this question.
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