Open Access
Translator Disclaimer
October 2002 Maxima of partial sums indexed by geometrical structures
Tiefang Jiang
Ann. Probab. 30(4): 1854-1892 (October 2002). DOI: 10.1214/aop/1039548374

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.

Citation

Download Citation

Tiefang Jiang. "Maxima of partial sums indexed by geometrical structures." Ann. Probab. 30 (4) 1854 - 1892, October 2002. https://doi.org/10.1214/aop/1039548374

Information

Published: October 2002
First available in Project Euclid: 10 December 2002

zbMATH: 1014.60024
MathSciNet: MR1944008
Digital Object Identifier: 10.1214/aop/1039548374

Subjects:
Primary: 28C15, 60B10, 60F10

Rights: Copyright © 2002 Institute of Mathematical Statistics

JOURNAL ARTICLE
39 PAGES


SHARE
Vol.30 • No. 4 • October 2002
Back to Top