Asymptotics of Weighted Empirical Processes of Linear Fields with Long-range Dependence
نویسندگان
چکیده
– We discuss the asymptotic behavior of weighted empirical processes of stationary linear random fields in Z 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. 2002 Éditions scientifiques et médicales Elsevier SAS MSC: 60F17; 60G60 RÉSUMÉ. – Nous étudions le comportement asymptotique du processus empirique pondéré pour un champ linéaire stationnaire à longue dépendance sur Z . Nous montrons que ce processus convenablement normalisé converge faiblement pour la topologie uniforme vers un processus dégénéré de la forme fZ, où Z est une variable normale standard et f est la densité de la marginale du champ considéré. 2002 Éditions scientifiques et médicales Elsevier SAS
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