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. 
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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/

[1] K. Prakhar, Raspredelenie prostykh chisel, Mir, M., 1967 | MR

[2] E. K. Titchmarsh, Teoriya dzeta-funktsii Rimana, Merkurii–Press, Cherepovets, 2000

[3] L. V. Rozovskii, “O nizhnei granitse veroyatnostei bolshikh uklonenii dlya vyborochnogo srednego pri vypolnenii usloviya Kramera”, Zap. nauchn. semin. POMI, 278, 2001, 208–224 | MR | Zbl

[4] O. E. Scherbakova, “Skorost skhodimosti dlya priraschenii sluchainykh polei”, Zap. nauchn. semin. POMI, 298, 2003, 304–315 | Zbl

[5] Paul Deheuvels, Luc Devroye, and James Lynch, “Exact Convergence Rate in the Limit Theorems of Erdös Rényi and Shepp”, Ann. of Probab., 14:1 (1986), 209–223 | DOI | MR | Zbl

[6] P. Deheuvels, J. Steinebach, “Exact Convergence Rate in Strong Approximation Laws for Large Increments of Partial Sums”, Probability Theory Related Fields, 1987, no. 76, 369–393 | DOI | MR | Zbl

[7] A. Frolov, A. Martikainen, J. Steinebach, “Erdös-Rényi-Shepp Type Laws in the Non-iid”, Studia Scientiarum Mathematicarum Hungarica, 33 (1997), 127–151 | MR | Zbl

[8] J. Steinebach, Wilfried Pfuhl, “On Precise Asymptotics for Erdös-Rényi Increments of Random Fields”, Pub. Inst. Stat. Univ., 33:2 (1988), 49–66