A LIMIT LAW FOR SUMS OF STOPPING TIME INDEXED SIGNUM FUNCTIONS
DOI:
https://doi.org/10.3126/jist.v31i1.86916Keywords:
law of the iterated logarithm, signum function, lacunary trigonometric series, martingale, stopping timesAbstract
A variety of limit laws describing the asymptotic behavior of functions have been developed in mathematics and statistics, among which the law of the iterated logarithm is considered one of the most significant. Motivated by these foundational results, we establish a LIL for sums of signum functions indexed by stopping times and determine a precise upper bound for the associated limit law.
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