论文标题
迭代的对数的法律，用于随机迪里奇莱特系列
Law of the iterated logarithm for a random Dirichlet series
论文作者
论文摘要
令$（x_n）_ {n \ in \ mathbb {n}} $为i.i.d的序列。带有分布的随机变量$ \ mathbb p（x_1 = 1）= \ mathbb p（x_1 = -1）= 1/2 $。令$ f（σ）= \ sum_ {n = 1}^\ infty x_nn^{ - σ} $。我们证明，以下几乎可以肯定地\ begin {equation*} \ limsup_ {σ\ to 1/2^+} \ frac {f（σ）} {\ sqrt {2 \ sqrt {2 \ mathbb e f（σ） \ end {equation*}
Let $(X_n)_{n\in \mathbb{N}}$ be a sequence of i.i.d. random variables with distribution $\mathbb P(X_1=1)=\mathbb P(X_1=-1)=1/2$. Let $F(σ)=\sum_{n=1}^\infty X_nn^{-σ}$. We prove that the following holds almost surely \begin{equation*} \limsup_{σ\to 1/2^+}\frac{F(σ)}{\sqrt{2\mathbb E F(σ)^2\log\log \mathbb E F(σ)^2}}=1. \end{equation*}
