Еxact rates in the Davis – Gut law of iterated logarithm for the first moment convergence of independent identically distributed random variables

• Date: 2017
• Main Authors: Xiao, X.-Y., Yin, H.-W., Сяо, Х.-І., Інь, Х.-В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1689
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $\{X, X_n, n \geq 1\}$ be a sequence of independent identically distributed random variables and let $S_n = \sum^n_{i=1} X_i$, $M_n = \max_{1\leq k\leq n} |S_k|$. For $r > 0$, let $a_n(\varepsilon)$ be a function of $\varepsilon$ such that $a_n(\varepsilon ) \mathrm{l}\mathrm{o}\mathr...