Weak convergence of self-normalized partial sums processes

Miklós Csörgő, Zhishui Hu

Let $\{X,X_n,n\ge 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0,S_n={\sum }_{i=1}^n{X}_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n…