Abstract
In this paper, for the partial sums with their maximums of a sequence of i.i.d. random variables, we show the precise rates in the general law of the iterated logarithm of a kind of weighted infinite series of the first moment convergence by using the strong approximation and point out the equivalent moment conditions.
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Xiao, X., Yin, H. Precise Rates in the Law of the Iterated Logarithm for the First Moment Convergence. Mediterr. J. Math. 11, 173–192 (2014). https://doi.org/10.1007/s00009-013-0351-4
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DOI: https://doi.org/10.1007/s00009-013-0351-4