Geodesic
On the rate of convergence in the strong law of large numbers for stationary processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 4, pp. 720-733 Cet article a éte moissonné depuis la source Math-Net.Ru

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If the covariance of a stationary (in a wide sense) process decreases with some rate, then means $\sigma_T$ (see (2)) converge to 0 a. s. We obtain the estimates for the rate of this convergence. These estimates are the best in a some sense. 
@article{TVP_1981_26_4_a3,
     author = {V. F. Gapo\v{s}kin},
     title = {On the rate of convergence in the strong law of large numbers for stationary processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {720--733},
     year = {1981},
     volume = {26},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a3/}
}
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V. F. Gapoškin. On the rate of convergence in the strong law of large numbers for stationary processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 4, pp. 720-733. http://geodesic.mathdoc.fr/item/TVP_1981_26_4_a3/