Geodesic
Asymptotics in the Baum--Katz formula for random fields
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 674-680

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In 1996, D. Deng established an analog of the Baum–Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained. 
@article{MZM_2006_79_5_a3,
     author = {S. V. Dil'man},
     title = {Asymptotics in the {Baum--Katz} formula for random fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {674--680},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a3/}
}
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S. V. Dil'man. Asymptotics in the Baum--Katz formula for random fields. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 674-680. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a3/