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On the rates of the almost sure convergence for self-normalized law of the iterated logarithm
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Let {X_i, i≥ 1} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote S_n=[수식]=max_(1≤ i≤ n)|S_i| and [수식]=[수식]. Then for d>-1, we showed that under some regularity conditions, [수식]=[수식]holds in this paper, where I{ · } denotes the indicator function.
Abstract
Let {X_i, i≥ 1} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote S_n=[수식]=max_(1≤ i≤ n)|S_i| and [수식]=[수식]. Then for d>-1, we showed that under some regularity conditions, [수식]=[수식]holds in this paper, where I{ · } denotes the indicator function.
참고문헌 (14)
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- "Precise rates in the law of the iterated logarithm"[URL]
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