关于u统计遍历定理的几个注释

IF 0.8 4区数学 Q2 MATHEMATICS Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI:10.5802/crmath.494

Herold G. Dehling, Davide Giraudo, Dalibor Volny

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引用次数: 0

摘要

本文研究具有平稳遍历数据的二阶u统计量的收敛性。我们将找到几乎确定和L 1收敛的充分条件，并给出一些反例，表明u统计量本身可能无法收敛:需要定心以及sup j≥2的有限性[|h(x1,X j)|]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some remarks on the ergodic theorem for U-statistics

In this note, we investigate the convergence of a U-statistic of order two having stationary ergodic data. We will find sufficient conditions for the almost sure and L 1 convergence and present some counter-examples showing that the U-statistic itself might fail to converge: centering is needed as well as finiteness of sup j≥2 𝔼[|h(X 1 ,X j )|].

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.