= Moderate deviation principle
{title2=$\frac{S_n-n\mu}{\sqrt n\,b_n},\quad b_n\to\infty,\quad b_n/\sqrt n\to0$}
= Moderate deviation
{synonym}
A <large deviation principle> for fluctuations larger than the usual <central limit theorem> scale but smaller than a fixed displacement of the empirical mean. For the displayed sum scaling, the natural <large-deviation speed> is $b_n^2$. Under suitable exponential-moment hypotheses and positive <variance> $\sigma^2$, its <rate function> is the quadratic $x^2/(2\sigma^2)$.
Back to article page
