English

Limiting behaviour of moving average processes genenrated by negatively dependent random variables under sub-linear expectations

Probability 2022-07-26 v1

Abstract

Let {Yi,<i<}\{Y_i,-\infty<i<\infty\} be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, {ai,<i<}\{a_i,-\infty<i<\infty\} be an absolutely summable sequence of real numbers. In this article, we study complete convergence and Marcinkiewicz-Zygmund strog law of large numbers for the partial sums of moving average processes {Xn=i=aiYi+n,n1}\{X_n=\sum_{i=-\infty}^{\infty}a_{i}Y_{i+n},n\ge 1\} based on the sequence {Yi,<i<}\{Y_i,-\infty<i<\infty\} of identically distributed, negatively dependent random variables under sub-linear expectations, complementing the result of [Chen, et al., 2009. Limiting behaviour of moving average processes under φ\varphi-mixing assumption. Statist. Probab. Lett. 79, 105-111].

Keywords

Cite

@article{arxiv.2207.11884,
  title  = {Limiting behaviour of moving average processes genenrated by negatively dependent random variables under sub-linear expectations},
  author = {Mingzhou Xu and Kun Cheng and Wangke Yu},
  journal= {arXiv preprint arXiv:2207.11884},
  year   = {2022}
}

Comments

13 pagess, submitted to Statistics and Probability letters

R2 v1 2026-06-25T01:11:20.085Z