Summary
A general integral test is established which refines the Jain-Pruitt Chung LIL for iid random variables. As a corollary we obtain that Chung's integral test for Brownian motion is valid for partial sums of iid random variables satisfyingEX 21{|X|≧t}=O((LLt) −1) ast→∞.
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Supported in part by NSF grant DMS 90-05804
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Einmahl, U. On the other law of the iterated logarithm. Probab. Th. Rel. Fields 96, 97–106 (1993). https://doi.org/10.1007/BF01195884
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DOI: https://doi.org/10.1007/BF01195884
Mathematics Subject Classification (1980)
- 60F15