Large Deviation Probabilities for Sums of Random Variables with Heavy or Subexponential Tails

Daren B. H. Cline, Tailen Hsing

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\…