Geodesic
Almost sure central limit theorem without logarithmic sums
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 110-119

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We investigate possible rates of convergence in almost sure CLT for sums of independent random variables and martingales. 
@article{ZNSL_2004_320_a8,
     author = {A. I. Martikainen},
     title = {Almost sure central limit theorem without logarithmic sums},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--119},
     publisher = {mathdoc},
     volume = {320},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a8/}
}
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A. I. Martikainen. Almost sure central limit theorem without logarithmic sums. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 110-119. http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a8/