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.
References
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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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DOI: https://doi.org/10.1007/BF01192960
Mathematics Subject Classification (1980)
- 60F15
- 60F17