Precise rates in the law of the iterated logarithm

2006/10/17 by Zhang Li, Li-Xin Zhang, Zhang, Li-Xin
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F15 #60G50 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60F15 #msc:60G50

paper · pdf · doi:10.48550/arxiv.math/0610519

arxiv created 2006/10/17 · openalex publication_date 2006/10/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X, X₁, X₂, ... be i.i.d. random variables, and let S_n=X₁+... + X_n be the partial sums and M_n=max_{k≤ n}|S_k| be the maximum partial sums. We give the sufficient and necessary conditions for a kind of limit theorems to hold on the convergence rate of the tail probabilities of both S_n and M_n. These results are related to the law of the iterated logarithm. The results of Gut and Spataru (2000) are special cases of ours.

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