The multiply iterated LIL is derived as the minimax boundary of a sequential-detection game whose equalizer prior is the Jeffreys prior selected by the Erdős-Kolmogorov integral test, yielding a closed-form 3/2 coefficient correction.
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The multiply iterated law of the iterated logarithm: game-theoretic foundations of sequential detection boundaries
The multiply iterated LIL is derived as the minimax boundary of a sequential-detection game whose equalizer prior is the Jeffreys prior selected by the Erdős-Kolmogorov integral test, yielding a closed-form 3/2 coefficient correction.