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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.

60G60 Random fields
60G15 Gaussian processes
60G10 Stationary stochastic processes
Full Text: DOI arXiv
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