Gaussian Markov triplets approached by block matrices

Multivariate normal distributions are described by a positive de nite matrix and if their joint distribution is Gaussian as well then it can be represented by a block matrix. The aim of this note is to study Markov triplets by using the block matrix technique. A Markov triplet is characterized by the form of its block covariance matrix and by the form of the inverse of this matrix. A strong subadditivity of entropy is proved for a triplet and equality corresponds to the Markov property. The results are applied to multivariate stationary homogeneous Gaussian Markov chains. 2000Mathematics Subject Classi cation. Primary 54C70, 60J05; Secondary 40C05, 60G15.

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