English

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

Probability 2024-02-20 v2 Statistics Theory Statistics Theory

Abstract

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

Keywords

Cite

@article{arxiv.2309.05988,
  title  = {Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences},
  author = {Davide Giraudo},
  journal= {arXiv preprint arXiv:2309.05988},
  year   = {2024}
}