Convergence of series connected with stationary sequences

Convergence almost everywhere of series $\sum a_k\xi_k$ is studied, where $\{\xi_k\}$ is a wide-sense stationary sequence (or a quasi-stationary sequence). Sufficient conditions are obtained for convergence of the series, which are also necessary in the class of all sequences $\{\xi_k\}$ having a given rate of decrease of the correlation function.
Analogous results are also valid for integrals of the type $\int_1^\infty a(t)\xi(t)\,dt$ where $\xi(t)$ is a wide-sense stationary process.
Bibliography: 12 titles.