The purpose of this paper is to show the strong consistency of the maximum pseudo-likelihood estimator for continuous state space stationary Gibbsian processes under fairly general conditions. Besides the maximum pseudo-likelihood estimator of Besag, we consider its extension, the maximum pseudo-likelihood of second order. The framework of our study is Ruelle's theory of superstable potential functions.
"Consistency of the Maximum Pseudo-Likelihood Estimator of Continuous State Space Gibbsian Processes." Ann. Appl. Probab. 5 (3) 603 - 612, August, 1995. https://doi.org/10.1214/aoap/1177004697