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 of a -statistic of order 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}
}