Strassen's law of the iterated logarithm

James D. Kuelbs

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 2, page 169-177
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Kuelbs, James D.. "Strassen's law of the iterated logarithm." Annales de l'institut Fourier 24.2 (1974): 169-177. <http://eudml.org/doc/74169>.

@article{Kuelbs1974,
abstract = {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.},
author = {Kuelbs, James D.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {169-177},
publisher = {Association des Annales de l'Institut Fourier},
title = {Strassen's law of the iterated logarithm},
url = {http://eudml.org/doc/74169},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Kuelbs, James D.
TI - Strassen's law of the iterated logarithm
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 2
SP - 169
EP - 177
AB - 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.
LA - eng
UR - http://eudml.org/doc/74169
ER -

References

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  1. [1] J. CHOVER, On Strassen's version of the log log law, Z. W. verw. Geb., Vol. 8 (1967), 83-90. Zbl0169.20901MR36 #930
  2. [2] R. DUDLEY, J. FELDMAN, L. LE CAM, On seminorms and probabilities, and abstract Wiener space, Annals of Math., Vol. 93 (1971), 390-408. Zbl0193.44603MR43 #4995
  3. [3] L. GROSS, Lectures in modern analysis and applications II, vol. 140, Lecture notes in mathematics, Springer-Verlag, New York. 
  4. [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. Zbl0292.60007MR50 #8628
  5. [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. Zbl0278.60052
  6. [6] V. SAZANOV, On the ω2 test, Sankhya (ser. A), Vol. 30 (1968), 204-209. 
  7. [7] V. SAZANOV, An improvement of a convergence-rate estimate, The Thy. of Prob. and its applications, Vol. 14 (1969), 640-651. Zbl0204.51205
  8. [8] V. STRASSEN, An invariance principle for the law of the iterated logarithm, Z. W. verw. Geb., Vol. 3 (1964), 211-226. Zbl0132.12903MR30 #5379
  9. [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. Zbl0298.60017

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