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Precise rates in the law of iterated logarithm for the moment of I.I.D. random variables
the law of iterated logarithm strong approximation truncation method i.i.d. random variables
2007/12/12
Let $\{X, X_n; n\ge 1\}$ be a sequence of i.i.d. random variables, ${\rm E} X=0$, ${\rm E} X^2=\sigma^2<\infty$. Set $S_n=X_1+X_2+\cdots+X_n$, $M_n=\max_{k\le n}|S_k|$, $n\ge 1$. Let $a_n=O(1/\log\log...