Une loi fonctionnelle uniforme du logarithme non standard pour les accroissements du processus empirique multivarié

Let (Zi)i⩾1 be an i.i.d. sequence being such that Z1 has a continuous, strictly positive density f on an open subset O⊂Rd. Let H⊂O be a closed subset with nonempty interior. Let (hn)n⩾1 denote a sequence of positive constants fulfilling, as n→∞, 0