Geodesic
Exact rate of convergence for increments of random fields
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 187-225

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The rate of convergence in strong limit theorems for maximal increments of random fields on parallelepipeds of big volume $a_{N}$ ($\lim\frac{a_{N}}{\log{N}}=\infty$, $\lim\frac{\log\frac{N}{a_{N}}}{\log_{2}N}=\infty$) is investigated. We consider random fields with finite moment generating function in right neighborhood of zero. 
@article{ZNSL_2004_320_a15,
     author = {O. E. Shcherbakova},
     title = {Exact rate of convergence for increments of random fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--225},
     publisher = {mathdoc},
     volume = {320},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a15/}
}
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O. E. Shcherbakova. Exact rate of convergence for increments of random fields. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 187-225. http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a15/