Abstract. Multivariate normal distributions are described by a positive definite 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.

AMS Subject Classification (1991): 54C70, 60J05; 40C05, 60G15

Keyword(s): normal distributions, Markov property, entropy, Schur complement, Hida--Cramér representation, Markov chain

Received March 15, 2008, and in revised form October 12, 2008. (Registered under 6077/2009.)