Doukhan, Paul; Lang, Gabriel; Surgailis, Donatas Asymptotics of weighted empirical processes of linear fields with long-range dependence. (English) Zbl 1016.60059 Ann. Inst. Henri Poincaré, Probab. Stat. 38, No. 6, 879-896 (2002). 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. Reviewer: B.L.S.Prakasa Rao (New Delhi) Cited in 24 Documents MSC: 60G60 Random fields 60F17 Functional limit theorems; invariance principles Keywords:linear random fields; long-range dependence PDFBibTeX XMLCite \textit{P. Doukhan} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 38, No. 6, 879--896 (2002; Zbl 1016.60059) Full Text: DOI Numdam EuDML