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 2005 |
All Science Journal Classification (ASJC) codes
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty