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.)
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