Persistence of iterated partial sums

Amir Dembo, Jian Ding, Fuchang Gao

Let $S_n^{(2)}$ denote the iterated partial sums. That is, $S_n^{(2)}=S_1+S_2+...+S_n$, where $S_i=X_1+X_2+...s+X_i$. Assuming $X_1,X_2,....,X_n$ are integrable, zero-mean, i.…