A supplement to the laws of large numbers and the large deviations

Deli Li, Yu Miao

Let $0<p<2$. Let $\{X,X_n;n\ge 1\}$ be a sequence of independent and identically distributed $\mathbf{B}$-valued random variables and set $S_{n} = \sum_{i=1}^{n}X_{i},~n…