### 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 language | English |
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Pages (from-to) | 329-345 |

Number of pages | 17 |

Journal | Acta Scientiarum Mathematicarum |

Volume | 75 |

Issue number | 1-2 |

Publication status | Published - 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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## Cite this

Ando, T., & Petz, D. (2009). Gaussian Markov triplets approached by block matrices.

*Acta Scientiarum Mathematicarum*,*75*(1-2), 329-345.