Summary
Clustering rates in Strassen's functional law of the iterated logarithm are determined for finite variance partial sum processes in one dimension. A general characterization of these rates, similar to one recently obtained for onedimensional Brownian motion, shows that relatively mild moment conditions on a partial sum process lead to high order clustering rates at certain points of the Strassen set.
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Supported in part by NSF Grant DMS-92-07248
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Einmahl, U., Goodman, V. Clustering behavior of finite variance partial sum processes. Probab. Th. Rel. Fields 102, 547–565 (1995). https://doi.org/10.1007/BF01198849
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DOI: https://doi.org/10.1007/BF01198849
Mathematics Subject Classification
- 60F15
- 60E07