Cluster sets for partial sums and partial sum processes

Uwe Einmahl, Jim Kuelbs

Let $X,X_1,X_2,\dots$ be i.i.d. mean zero random vectors with values in a separable Banach space $B$, $S_n=X_1+\cdots +X_n$ for $n\ge 1$, and assume $\{c_n:n\ge 1\}$ is a suitably re…