Lower Functions of Empirical Processes and Brownian Sheets M.A. Lifshits and Z. Shi
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 infinitedimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in the book of Shorack and Wellner.
Lower Functions of Empirical Processes and Brownian Sheets M.A. ...
M.A. Lifshits and Z. Shi. We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process.
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