Sectorial convergence of U-statistics

Anda Gadidov

doi:10.1214/009117904000001080

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Home > Journals > Ann. Probab. > Volume 33 > Issue 2 > Article

March 2005 Sectorial convergence of U-statistics

Anda Gadidov

Ann. Probab. 33(2): 816-822 (March 2005). DOI: 10.1214/009117904000001080

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Abstract

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 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.