Gaussian Markov triplets approached by block matrices

Tsuyoshi Ando, Dénes Petz

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)329-345
Number of pages17
JournalActa Scientiarum Mathematicarum
Volume75
Issue number1-2
Publication statusPublished - Dec 1 2009

Keywords

  • Entropy
  • Hida-Cramér representation
  • Markov chain
  • Markov property
  • Normal distributions
  • Schur complement

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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