English

Complete moment convergence of moving average processes for $m$-widely acceptable sequence under sub-linear expectations

Probability 2024-03-28 v1

Abstract

In this article, the complete moment convergence for the partial sum of moving average processes {Xn=i=aiYi+n,n1}\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\} is estabished under some proper conditions, where {Yi,<i<}\{Y_i,-\infty<i<\infty\} is a sequence of mm-widely acceptable (mm-WA) random variables, which is stochastically dominated by a random variable YY in sub-linear expectations space (Ω,\HH,\ee)(\Omega,\HH,\ee) and {ai,<i<}\{a_i,-\infty<i<\infty\} is an absolutely summable sequence of real numbers. The results extend the relevant results in probability space to those under sub-linear expectations.

Keywords

Cite

@article{arxiv.2403.18304,
  title  = {Complete moment convergence of moving average processes for $m$-widely acceptable sequence under sub-linear expectations},
  author = {Mingzhou Xu and Xuhang Kong},
  journal= {arXiv preprint arXiv:2403.18304},
  year   = {2024}
}

Comments

16 pages,submitted to Journal of Inequalities and Applications

R2 v1 2026-06-28T15:35:07.740Z