Strassen's law of the iterated logarithm
Annales de l'Institut Fourier, Volume 24 (1974) no. 2, p. 169-177

Strassen’s functional form of the law of the iterated logarithm is formulated for partial sums of random variables with values in a strict inductive limit of Frechet spaces of Hilbert space type. The proof depends on obtaining Berry-Essen estimates for Hilbert space valued random variables.

Il s’agit d’établir la forme fonctionnelle de Strassen de la loi du logarithme itéré pour les sommes partielles de variables aléatoires à valeurs dans la limite inductive stricte d’espaces de Fréchet, qui sont de type d’espace d’Hilbert. La démonstration dépend de l’obtention des estimations de Barry-Esssen pour les variables aléatoires à valeurs dans un espace d’Hilbert.

@article{AIF_1974__24_2_169_0,
     author = {Kuelbs, James D.},
     title = {Strassen's law of the iterated logarithm},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {24},
     number = {2},
     year = {1974},
     pages = {169-177},
     doi = {10.5802/aif.510},
     zbl = {0275.60037},
     mrnumber = {53 \#9356},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1974__24_2_169_0}
}
Kuelbs, James D. Strassen's law of the iterated logarithm. Annales de l'Institut Fourier, Volume 24 (1974) no. 2, pp. 169-177. doi : 10.5802/aif.510. http://www.numdam.org/item/AIF_1974__24_2_169_0/

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