Limit theorem for some functionals of random walks

Let $\xi_,\xi_2,\dots,\xi_n,\dots$ be a sequence of independent random variables with the same distributions, $S_n=\sum_{j=1}^n\xi_j$ and let $f(x,y)$ be a measurable function. Limit theorems for the distributions of sums $\sum_{j=0}^{n-1}\sum_{k=0}^{n-1}S(S_jS_k)$ are obtained.