Maximal inequalities for centered norms of sums of independent random vectors

Rafał Latała

Let $X_1,X_2,\dots ,X_n$ be independent random variables and $S_k={\sum }_{i=1}^k{X}_i$. We show that for any constants $a_k$, \[ \Pr(\max_{1\leq k\leq n}||S_{k}|-a_{k}|>11t)\leq 30 \m…