Summary
Kuelbs (1975) established a Kolmogorov-Erdös-Petrowski type integral test for lower and upper classes in the law of the iterated logarithm for sums of i.i.d. Hilbert space valued Gaussian mean zero random variables. We show that this integral test remains valid for sums of i.i.d. pregaussian mean zero random variables satisfying an additional (very mild) assumption.
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Einmahl, U. A note on the law of the iterated logarithm in Hilbert space. Probab. Th. Rel. Fields 82, 213–223 (1989). https://doi.org/10.1007/BF00354760
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DOI: https://doi.org/10.1007/BF00354760
Keywords
- Hilbert Space
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Iterate Logarithm