Pré-Publication, Document De Travail Année : 2023

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

Résumé

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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Dates et versions

hal-04202655 , version 1 (11-09-2023)
hal-04202655 , version 2 (16-02-2024)

Identifiants

Citer

Davide Giraudo. Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences. 2023. ⟨hal-04202655v1⟩
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