Doukhan, Paul; Surgailis, Donatas 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 C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 1, 87-92 (1998). 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) Cited in 16 Documents MSC: 60F05 Central limit and other weak theorems Keywords:central limit theorem; short memory linear process; empirical distribution PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{D. Surgailis}, C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 1, 87--92 (1998; Zbl 0948.60012) Full Text: DOI