Space-time models based on random fields with local interactionsSpace-time models based on random fields with local interactions Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2018-10-102016enThe analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving "effective equations of motion", which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.http://creativecommons.org/licenses/by/4.0/International Journal of Modern Physics B3015 Christopoulos Dionysios Χριστοπουλος Διονυσιος Tsantili Ivi Τσαντιλη Ηβη World Scientific Publishing Correlation modeling Linear response Local interactions Maximum entropy Space-time models