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.
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.
@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}, volume = {24}, year = {1974}, pages = {169-177}, doi = {10.5802/aif.510}, mrnumber = {53 \#9356}, zbl = {0275.60037}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1974__24_2_169_0} }
Kuelbs, James D. Strassen's law of the iterated logarithm. Annales de l'Institut Fourier, Tome 24 (1974) pp. 169-177. doi : 10.5802/aif.510. http://gdmltest.u-ga.fr/item/AIF_1974__24_2_169_0/
[1] On Strassen's version of the log log law, Z. W. verw. Geb., Vol. 8 (1967), 83-90. | MR 36 #930 | Zbl 0169.20901
,[2] On seminorms and probabilities, and abstract Wiener space, Annals of Math., Vol. 93 (1971), 390-408. | MR 43 #4995 | Zbl 0193.44603
, , ,[3] Lectures in modern analysis and applications II, vol. 140, Lecture notes in mathematics, Springer-Verlag, New York.
,[4] Some results for probability measures on linear topological vector spaces with an application to Strassen's log log law, Journal of Functional Analysis, Vol. 14 (1973), 28-43. | MR 50 #8628 | Zbl 0292.60007
,[5] The law of the iterated logarithm for Brownian motion in a Banach space, to appear in The Trans. Amer. Math. Soc. | Zbl 0278.60052
and ,[6] On the ω2 test, Sankhya (ser. A), Vol. 30 (1968), 204-209.
,[7] An improvement of a convergence-rate estimate, The Thy. of Prob. and its applications, Vol. 14 (1969), 640-651. | Zbl 0204.51205
,[8] An invariance principle for the law of the iterated logarithm, Z. W. verw. Geb., Vol. 3 (1964), 211-226. | MR 30 #5379 | Zbl 0132.12903
,[9] Berry-Essen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm, to appear in the Annals of Probability. | Zbl 0298.60017
and ,