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.

@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},
     pages = {169--177},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
     number = {2},
     year = {1974},
     doi = {10.5802/aif.510},
     zbl = {0275.60037},
     mrnumber = {53 #9356},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.510/}
}
TY  - JOUR
AU  - Kuelbs, James D.
TI  - Strassen's law of the iterated logarithm
JO  - Annales de l'Institut Fourier
PY  - 1974
SP  - 169
EP  - 177
VL  - 24
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.510/
DO  - 10.5802/aif.510
LA  - en
ID  - AIF_1974__24_2_169_0
ER  - 
%0 Journal Article
%A Kuelbs, James D.
%T Strassen's law of the iterated logarithm
%J Annales de l'Institut Fourier
%D 1974
%P 169-177
%V 24
%N 2
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.510/
%R 10.5802/aif.510
%G en
%F AIF_1974__24_2_169_0
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. https://aif.centre-mersenne.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

Cité par Sources :