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On développe une approche générale du théorème limite centrale presque-sûre pour les martingales vectorielles quasi-continues à gauche convenablement normalisées dont on dégage une extension quadratique et un nouveau théorème de la limite centrale. L'application de ce résultat à l'estimation de la variance d'un processus à accroissements indépendants et stationnaires illustre l'usage qu'on peut en faire en statistique.
We give limit theorems specifying weak and
strong rates of convergence associated to a quadratic extension of the
martingale almost-sure central limit theorem. Some typical examples are
discussed to illustrate how to make use of them in statistic.
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