Geodesic
Exponential bounds for smooth fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 230-235

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Theorem of Section 3 gives exponentially decreasing bounds on sup norm large deviation probabilities for sums of independent random fields over the $k$-dimensional unit cube. Summands are supposed to have sufficiently smooth sample functions (4), (7) and satisfy Cramer's type conditions (5), (6). Proofs are based on Sobolev's imbedding theorems. 
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     author = {V. V. Yurinskii},
     title = {Exponential bounds for smooth fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a27/}
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V. V. Yurinskii. Exponential bounds for smooth fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 230-235. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a27/