Hi, could it be that they consider spatial data on a lattice? These formulations remind me of the "Analysis and modelling of lattice data" chapter from the book "Analyizing ecological Data" from Alain F. Zuur. These models are defined analogeous to autocorrelation models for time series, i.e., they assume that the space is a priori divided by a lattice and data are only given at the gridpoints of this lattice. This leads e.g. to "Simultaneous auto-regressive (SAR) Models" or "Spatial Moving Average (SMA) Models", analogeous to "AR" and "MA" models for time series. If you have spatially continuous data, analogeous models are Kriging models with different types of variograms.