Denote the joint pdf of the n-variate normal random vector X with mean p and variance matrix C by +,(x I p , E). Theorem: Let e be the n-variate normal random vector with mean 0 and covariance matrix 6'1. Then, the joint pdf minimizing the time-domain KL information number subject to the first p + 1 autocovariance constraints a (0) = (Yo, a(1) = (Y I , * * ,. (p) = ap is +,(e10, %I. Proof: The KL information number can be decomposed into two parts: The first integral of the RHS is greater than or e ual to 0 by Jensen's inequality. It equals 0 if the joint pdf is ,,,(eqO, V n) .

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