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Théorème de limite centrale fonctionnelle pour la fonction de répartition empirique d’un processus linéaire à mémoire courte. (Functional central limit theorem for the empirical process of short memory linear processes.) (English. Abridged French version) Zbl 0948.60012

Consider a strictly stationary causal linear sequence \(\{X_j,\;j\in {\mathbb Z}\}\), where \(X_j=\sum_{t\geq 0}a_t\xi_{j-t}\), for \(j\in {\mathbb Z}\), \(\{\xi_j,\;j\in{\mathbb Z}\}\) is an independently and identically distributed sequence and \(a_j,\;j\geq 0\), are (nonrandom) weights such that \(\sum_{t\geq 0}|a_t|^\gamma<\infty\) and \(E|\xi_0|^{4\gamma}<\infty\) for some \(\gamma\in(0,\infty]\). Assume that \(v\text{ var}(X_j)<\infty\) and the process becomes a short memory linear process. The authors prove the functional central limit theorem for the empirical distribution function of this process under the condition that \(|E\exp{iui_0}|\leq C/(1+|u|)^{\Delta}\), for any \(u\in {\mathbb R}\), some \(C<\infty\), and \(1/2<\Delta\leq 1\).
Reviewer: Y.Wu (North York)

MSC:

60F05 Central limit and other weak theorems
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