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Rates of clustering in Strassen's LIL for partial sum processes
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  • Published: December 1993

Rates of clustering in Strassen's LIL for partial sum processes

  • Uwe Einmahl1 &
  • David M. Mason2 

Probability Theory and Related Fields volume 97, pages 479–487 (1993)Cite this article

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  • 9 Citations

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Summary

We provide a detailed description of the rate of clustering in Strassen's functional law of the iterated logarithm for partial sum processes. Necessary and sufficient conditions are given for certain clustering rates in terms of moment-type conditions. In the process, we also derive a new strong approximation of sums of iid random variables by a Wiener process.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Uwe Einmahl

  2. Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA

    David M. Mason

Authors
  1. Uwe Einmahl
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  2. David M. Mason
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Additional information

Partially supported by NSF Grant DMS 90-05804

Partially supported by NSF Grant DMS 92-11809

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Einmahl, U., Mason, D.M. Rates of clustering in Strassen's LIL for partial sum processes. Probab. Th. Rel. Fields 97, 479–487 (1993). https://doi.org/10.1007/BF01192960

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  • Received: 16 February 1993

  • Revised: 14 April 1993

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01192960

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Mathematics Subject Classification (1980)

  • 60F15
  • 60F17
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