Author

Peng Zhang

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Preprint Jul 2026

Sharp small-deviation inequalities for sums of independent nonnegative random variables

Let $(X_1,\ldots,X_n)$ be independent nonnegative random variables with $\mathbb{E} X_i\le1$, and write $S=\sum_iX_i$. For $\delta>0$, we prove that \[ \mathbb{P}\left(S<\mathbb{E} S+\delta\right)\ge b_{n,\delta}, \] where $b_{n,\delta}=\delta(n/(n+\delta))^n$ for $0<\delta<1$ and $b_{n,\delta}=(1-1/(n+\delta))^n$ for...

Weibo Fu, Yanjun Han, Guanyang Wang et al. · 7 citations · ⚡1