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Asymptotics of weighted empirical processes of linear fields with long-range dependence. (English) Zbl 1016.60059

Authors’ summary: We discuss the asymptotic behavior of weighted empirical processes of stationary linear random fields in \(\mathbb{Z}^d\) with long-range dependence. It is shown that an appropriately standardized empirical process converges weakly in the uniform topology to a degenerated process of the form \(fZ\), where \(Z\) is a standard normal random variable and \(f\) is the marginal probability density of the underlying random field.

MSC:

60G60 Random fields
60F17 Functional limit theorems; invariance principles
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