Geodesic
Convergence of series connected with stationary sequences
Izvestiya. Mathematics , Tome 9 (1975) no. 6, pp. 1297-1321

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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. 
@article{IM2_1975_9_6_a7,
     author = {V. F. Gaposhkin},
     title = {Convergence of series connected with stationary sequences},
     journal = {Izvestiya. Mathematics },
     pages = {1297--1321},
     publisher = {mathdoc},
     volume = {9},
     number = {6},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a7/}
}
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V. F. Gaposhkin. Convergence of series connected with stationary sequences. Izvestiya. Mathematics , Tome 9 (1975) no. 6, pp. 1297-1321. http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a7/