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}, 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 -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.510/
[1] On Strassen's version of the log log law, Z. W. verw. Geb., Vol. 8 (1967), 83-90. | MR | Zbl
,[2] On seminorms and probabilities, and abstract Wiener space, Annals of Math., Vol. 93 (1971), 390-408. | MR | Zbl
, , ,[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 | Zbl
,[5] The law of the iterated logarithm for Brownian motion in a Banach space, to appear in The Trans. Amer. Math. Soc. | Zbl
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
,[8] An invariance principle for the law of the iterated logarithm, Z. W. verw. Geb., Vol. 3 (1964), 211-226. | MR | Zbl
,[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
and ,Cited by Sources: