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Exact rate of convergence in Strassen's law of the interated logarithm

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Abstract

We investigate the upper limiting behavior of the distance of the normalize trajectories of a Wiener process from Strassen's class. It is shown that the right rate is (log logT)−2/3, improving previous results by the author and by Goodman and Kuelbs.(2,3)

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References

  1. Bolthausen, E. (1978). On the speed of convergence in Strassen's law of the iterated logarithm.Ann. Prob. 6, 668–672.

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  2. Goodman, V., and Kuelbs, J. (1991). Rate of clustering in Strassen's LIL for Brownian motion.J. Theor. Prob. 4, 285–310.

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  3. Goodman, V., and Kuelbs, J. (1989). Rate of clustering for some Gaussian self-similar processes.Prob. Theor. Rel. Fields (to appear).

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  5. Strassen, V. (1964). An invariance principle for the law of the iterated logarithm.Z. Wahrsch. verw. Gebiete 3, 211–226.

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  1. Institut für Statistik und Warscheinlichkeitstheorie TU, Vienna, Austria

    Karl Grill

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  1. Karl Grill
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Grill, K. Exact rate of convergence in Strassen's law of the interated logarithm. J Theor Probab 5, 197–204 (1992). https://doi.org/10.1007/BF01046785

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  • DOI: https://doi.org/10.1007/BF01046785

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