论文标题
具有沉重或次指数尾巴的随机变量总和的较大偏差概率
Large Deviation Probabilities for Sums of Random Variables with Heavy or Subexponential Tails
论文作者
论文摘要
令$ s_n $为具有分配$ f $的独立随机变量的总和。在假设$ - \ log（1-f（x））$正在缓慢变化的假设下，条件为$$ \ lim_ {n \ to \ infty} \ sup_ {s \ ge t_n} \ left | {p [s_n> s] \ vos n（1-f（s））} - 1 \ right | = 0 $$。这些条件扩展并加强了一系列先前的结果。此外，还证明了与次数分布的连接。也就是说，$ f $在且仅当上述条件适用于某些$ t_n $和$$时 \ lim_ {t \ to \ infty} {1-f（t+x）\ over 1-f（t）} = 1 \ quad \ text {对于每个真正的$ x $。} $$
Let $S_n$ be the sum of independent random variables with distribution $F$. Under the assumption that $-\log(1-F(x))$ is slowly varying, conditions for $$ \lim_{n\to\infty}\sup_{s\ge t_n}\left|{P[S_n>s]\over n(1-F(s))}-1\right| =0 $$ are given. These conditions extend and strengthen a series of previous results. Additionally, a connection with subexponential distributions is demonstrated. That is, $F$ is subexponential if and only if the condition above holds for some $t_n$ and $$ \lim_{t\to\infty}{1-F(t+x)\over 1-F(t)} = 1 \quad\text{for each real $x$.}$$
