Department
Physics
Document Type
Article
Publication Date
3-2005
Embargo Period
8-31-2017
Abstract
In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in ℤd+ is equivalent to convergence along the diagonal of ℤd+, as it is considered in Latała and Zinn [Ann. Probab. 28 (2000) 1908–1924]. Comparisons with similar results for sums of multi-indexed i.i.d. random variables are also made.
Journal Title
The Annals of Probability
Journal ISSN
0091-1798
Volume
33
Issue
2
First Page
816
Last Page
822
Digital Object Identifier (DOI)
10.1214/009117904000001080