Markov approximation of homogeneous lattice random fields

B. M. Gurevich; A. A. Tempelman

doi:10.1007/s00440-004-0383-6

Markov approximation of homogeneous lattice random fields

B. M. Gurevich, A. A. Tempelman

Research output: Contribution to journal › Article

3 Scopus citations

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)
Pages (from-to)	519-527
Number of pages	9
Journal	Probability Theory and Related Fields
Volume	131
Issue number	4
DOIs	https://doi.org/10.1007/s00440-004-0383-6
State	Published - Apr 1 2005

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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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

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AB - 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.

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