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Strassen's iterated logarithm law for Hilbert space valued random variables

Published online by Cambridge University Press:  01 July 2016

Wim Vervaat
Wim Vervaat*
Affiliation:
University of Amsterdam
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Abstract

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Type
I. Invited Review and Research Papers
Information
Advances in Applied Probability , Volume 7 , Issue 2 , June 1975 , pp. 242 - 244
Copyright
Copyright © Applied Probability Trust 1975 

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References

Chover, J. (1967) On Strassen's version of the loglog law. Z. Wahrscheinlichkeitsth. 8, 83–90.Google Scholar
Kuelbs, J. and Kurtz, T. (1974) Berry-Esséen estimates in Hilbert space and an application to the law of the iterated logarithm. Ann. Probability 2, 387–407.Google Scholar
Kuelbs, J. (1974) A strong convergence theorem for Banach space valued random variable. To appear.Google Scholar
Strassen, V. (1964) An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitsth. 3, 211–226.Google Scholar
Strassen, V. (1967) Almost sure behavior of sums of independent random variables and martingales. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 2, 315–343.Google Scholar
Wichura, M. J. (1973) Some Strassen-type laws of the iterated logarithm for multiparameter stochastic processes with independent increments. Ann. Probability 1, 272–296.Google Scholar