Analogs of the arcsine distribution for sequences linearly generated by independent random variables

Let $\{\xi_k\}$, $k=\dots,-1,0,1,\dots$, be a sequence of independent identically distributed random variables with $E_{\xi_k}=0$, $D_{\xi_k}=\sigma^2<\infty$. Let $\{c_k\}$ be a numerical sequence such that $\sum^\infty_{-\infty}c^2_k<\infty$ Let
$$ X_n=\sum^\infty_{-\infty}c_{k-n}\xi_k,\quad S_n=\sum^n_1X_k. $$
This article investigates the limit behavior of the distributions of functionals of the following type:
$$ \nu_k=\dfrac1n\sum^n_1h(S_k), $$
where $h$ is a bounded function on $R^1$.