Sectorial convergence of U-statistics

• 成果类型: Article
• 署名作者: Gadidov, A
• 署名单位: University System of Georgia; Kennesaw State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000001080
• 发表日期: 2005
• 页码: 816-822
• 关键词: random-variables; large numbers; strong laws; sums; inequalities; PRODUCTS

摘要

In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in Z(+)(d) is equivalent to convergence along the diagonal of Z(+)(d), as it is considered in Latala and Zinn [Ann. Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums of multiindexed i.i.d. random variables are also made.