Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences

Davide Giraudo

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arXiv · 2309.05988

Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences

Davide Giraudo

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Abstract

In this note, we give sufficient conditions for the almost sure and the convergence in $\mathbb{L}^p$ of a $U$-statistic of order $m$ built on a strictly stationary but not necessarily ergodic sequence.

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Davide Giraudo. 2023-09-12. Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences. https://arxiv.org/abs/2309.05988

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