Scaling transition for long-range dependent Gaussian random fields

In Puplinskaitė and Surgailis (2014) we introduced the notion of scaling transition for stationary random fields XX on Z2Z2 in terms of partial sums limits, or scaling limits, of XX over rectangles whose sides grow at possibly different rate. The present paper establishes the existence of scaling transition for a natural class of stationary Gaussian random fields on Z2Z2 with long-range dependence. The scaling limits of such random fields are identified and characterized by dependence properties of rectangular increments.