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

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.

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Kuelbs, James D. Strassen's law of the iterated logarithm. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 169-177. doi : 10.5802/aif.510. http://archive.numdam.org/articles/10.5802/aif.510/

[1] J. Chover, On Strassen's version of the log log law, Z. W. verw. Geb., Vol. 8 (1967), 83-90. | MR | Zbl

[2] R. Dudley, J. Feldman, L. Le Cam, On seminorms and probabilities, and abstract Wiener space, Annals of Math., Vol. 93 (1971), 390-408. | MR | Zbl

[3] L. Gross, Lectures in modern analysis and applications II, vol. 140, Lecture notes in mathematics, Springer-Verlag, New York.

[4] J. Kuelbs, 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 | Zbl

[5] J. Kuelbs and R. Le Page, The law of the iterated logarithm for Brownian motion in a Banach space, to appear in The Trans. Amer. Math. Soc. | Zbl

[6] V. Sazanov, On the ω2 test, Sankhya (ser. A), Vol. 30 (1968), 204-209.

[7] V. Sazanov, An improvement of a convergence-rate estimate, The Thy. of Prob. and its applications, Vol. 14 (1969), 640-651. | Zbl

[8] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. W. verw. Geb., Vol. 3 (1964), 211-226. | MR | Zbl

[9] J. Kuelbs and T. Kurtz, Berry-Essen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm, to appear in the Annals of Probability. | Zbl

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