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This article is cited in 4 scientific papers (total in 4 papers)
Lower functions of empirical processes and Brownian sheets
M. A. Lifshitsa, Zh. Shib a University of Sciences and Technologies
b Université Pierre & Marie Curie, Paris VI
Abstract:
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.
Received: 30.09.2002
Citation:
M. A. Lifshits, Zh. Shi, “Lower functions of empirical processes and Brownian sheets”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 321–339; Theory Probab. Appl., 48:2 (2004), 273–287
Linking options:
https://www.mathnet.ru/eng/tvp287https://doi.org/10.4213/tvp287 https://www.mathnet.ru/eng/tvp/v48/i2/p321
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Abstract page: | 344 | Full-text PDF : | 161 | References: | 64 |
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