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A sufficient condition for asymptotic normality of the normalized quadratic form Ψn(f,g)
Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 971-975.

Many sufficient conditions of asymptotic normality of the normalized quadratic form Ψn(f,g) have been proposed since 1958. The less restrictive was given in the paper of L. Giraitis and D. Surgailis (1990). Using a linear operator approach, it is possible to produce an even less restrictive sufficient condition on the couple of functions (f,g).

Des conditions suffisantes de normalité asymptotique de la forme quadratique standardisée Ψn(f,g) se sont succédées depuis 1958. La moins restrictive fût proposée par L. Giraitis et D. Surgailis en 1990. En abordant le problème sous l'angle des opérateurs linéaires, il est possible de produire une condition suffisante encore moins restrictive sur le couple de fonctions (f,g).

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DOI: 10.1016/j.crma.2006.04.022
Solev, Valentin 1; Gerville-Reache, Léo 2

1 Steklov Mathematical Institute, St Petersbourg, Russia
2 Statistique mathématique, université Victor-Segalen, 146, rue Léo-Saignat, 33076 Bordeaux, France
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Solev, Valentin; Gerville-Reache, Léo. A sufficient condition for asymptotic normality of the normalized quadratic form $ {\Psi }_{n}(f,g)$. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 971-975. doi : 10.1016/j.crma.2006.04.022. http://www.numdam.org/articles/10.1016/j.crma.2006.04.022/

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