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Scaling transition for long-range dependent Gaussian random fields. (English) Zbl 1317.60062
Summary: In [D. Puplinskaitė and D. Surgailis, “Aggregation of autoregressive random fields and anisotropic long-range dependence”, Preprint,
urlarxiv:1303.2209v3] we introduced the notion of scaling transition for stationary random fields \(X\) on \(\mathbb{Z}^2\) in terms of partial sums limits, or scaling limits, of \(X\) over rectangles whose sides grow at possibly different rate. The present paper establishes the existence of scaling transitions for a natural class of stationary Gaussian random fields on \(\mathbb{Z}^2\) with long-range dependence. The scaling limits of such random fields are identified and characterized by dependence properties of rectangular increments.

MSC:
60G60 Random fields
60G15 Gaussian processes
60G10 Stationary stochastic processes
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