Maxima of partial sums indexed by geometrical structures
Tiefang Jiang
Source: Ann. Probab. Volume 30, Number 4
(2002), 1854-1892.
Abstract
The maxima of partial sums indexed by squares and rectangles over lattice points and random cubes are studied in this paper. For some of these problems, the dimension ($d=1, d=2$ and $d \geq 3$) significantly affects the limit behavior of the maxima. However, for other problems, the maxima behave almost the same as their one-dimensional counterparts. The tools for proving these results are large deviations, the Chen-Stein method, number theory and inequalities of empirical processes.
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Keywords: Maxima; Chen-Stein method; number theory; large deviations; inequalities of empirical processes
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1039548374
Digital Object Identifier: doi:10.1214/aop/1039548374
Mathematical Reviews number (MathSciNet): MR1944008
Zentralblatt MATH identifier: 1014.60024
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MINNEAPOLIS, MN 55455 E-MAIL: tjiang@stat.umn.edu
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