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Power-law correlations and other models with long-range dependence on a lattice. (English) Zbl 1041.60046

The paper introduces the definition of long-range dependence for stationary random fields on \(Z^2.\) Power-law correlation structure is investigated. The connection between short-range dependent correlation functions and absolutely summable double sequences is shown. Numerous examples are given.

MSC:

60G60 Random fields
60G10 Stationary stochastic processes
62M30 Inference from spatial processes
62M15 Inference from stochastic processes and spectral analysis
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