A CENTRAL-LIMIT-THEOREM FOR CONDITIONALLY CENTERED RANDOM-FIELDS WITHAN APPLICATION TO MARKOV-FIELDS

We prove a central limit theorem for conditionally centred random fiel ds, under a moment condition and strict positivity of the empirical va riance per observation. We use a random normalization, which fits non- stationary situations. The theorem applies directly to Markov random f ields, including the cases of phase transition and lack of stationarit y. One consequence is the asymptotic normality of the maximum pseudo-l ikelihood estimator for Markov fields in complete generality.