Geodesic
Lower functions of empirical processes and Brownian sheets
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 2, pp. 321-339

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We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process via integral criteria. Our result for the Brownian sheet can be viewed as a solution, in a very special case (the general case remains an open question), of the following problem: find the escape rate of infinite-dimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in [G. R. Shorack and J. A. Wellner, Wiley, New York, 1986.].
Keywords: rate of escape, empirical process, infinite-dimensional Brownian motion, Brownian sheet, lower function. 
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     author = {M. A. Lifshits and Zh. Shi},
     title = {Lower functions of empirical processes and {Brownian} sheets},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {321--339},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_2_a5/}
}
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M. A. Lifshits; Zh. Shi. Lower functions of empirical processes and Brownian sheets. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 2, pp. 321-339. http://geodesic.mathdoc.fr/item/TVP_2003_48_2_a5/