### Abstract

We refine some well-known approximation theorems in the theory of homogeneous lattice random fields. In particular we prove that every translation invariant Borel probability measure μ on the space X of finite-alphabet configurations on ℤ can be weakly approximated by Markov measures μ _{n} with supp(μ _{n} )=X and with the entropies h(μ _{n} )→h(μ). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version of this theorem.

Original language | English (US) |
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Pages (from-to) | 519-527 |

Number of pages | 9 |

Journal | Probability Theory and Related Fields |

Volume | 131 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2005 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Gurevich, B. M., & Tempelman, A. A. (2005). Markov approximation of homogeneous lattice random fields.

*Probability Theory and Related Fields*,*131*(4), 519-527. https://doi.org/10.1007/s00440-004-0383-6