Geodesic
Local and global upper functions for random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 4, pp. 755-764

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We introduce and calculate the local and global upper functions for arbitrary, i.e., not necessarily Gaussian, random fields. Only the Cramer condition is assumed to be fulfilled for the fields under consideration. Despite the generality we show by examples that the results obtained are precise for the Gaussian fields studied earlier. Possible applications are described.
Keywords: random field, local and global modules of continuity, Young–Fenchel transform, metric entropy, exponential estimate. 
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     author = {S. A. Egishyants and E. I. Ostrovskii},
     title = {Local and global upper functions for random fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {755--764},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_4_a2/}
}
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S. A. Egishyants; E. I. Ostrovskii. Local and global upper functions for random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 4, pp. 755-764. http://geodesic.mathdoc.fr/item/TVP_1996_41_4_a2/