Ja n 20 04 Chains with complete connections : General theory , uniqueness , loss of memory and mixing properties

  title={Ja n 20 04 Chains with complete connections : General theory , uniqueness , loss of memory and mixing properties},
  author={Roberto Fern{\'a}ndez and Gr{\'e}gory Maillard},
We introduce an statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail σ-algebra, short-range correlations, realization via infinite-volume limits and ergodicity. (ii) Two new sufficient conditions for the uniqueness of the consistent chain. The first one is a transcription of a criterion due to Georgii for one-dimensional Gibbs measures, and the second one corresponds… CONTINUE READING

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