Maxima of partial sums indexed by geometrical structures
Jiang, Tiefang
Ann. Probab., Tome 30 (2002) no. 1, p. 1854-1892 / Harvested from Project Euclid
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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.
Publié le : 2002-10-14
Classification:  Maxima,  Chen-Stein method,  number theory,  large deviations,  inequalities of empirical processes,  60F10,  28C15,  60B10 
@article{1039548374,
     author = {Jiang, Tiefang},
     title = {Maxima of partial sums indexed by geometrical structures},
     journal = {Ann. Probab.},
     volume = {30},
     number = {1},
     year = {2002},
     pages = { 1854-1892},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1039548374}
}

Jiang, Tiefang. Maxima of partial sums indexed by geometrical structures. Ann. Probab., Tome 30 (2002) no. 1, pp.  1854-1892. http://gdmltest.u-ga.fr/item/1039548374/