On the large deviation principle for stationary weakly dependent random fields
Using a new criterion for the large deviation principle, the author proves the large deviation principle for the empirical field of a stationary \(\mathbb{Z}^ d\)-indexed random field. Different strong mixing assumptions are used to obtain the results for a compact or Polish space- valued random field. These assumptions allow to give a detailed description of the resulting rate function. Applications to empirical fields of Markov chains with a compact (or Polish) state space or to Gibbs fields with a countable state space and summable interaction potential are given.
scientific article; zbMATH DE number 89799