Complete moment convergence of moving average processes generated by $ m $-widely acceptable sequences under sub-linear expectations
Abstract
In this article, the complete moment convergence for the partial sum of moving average processes $ \{X_n = \sum_{i = -\infty}^{\infty}a_iY_{i+n}, n\ge 1\} $ is established under some proper conditions, where $ \{Y_i, -\infty < i < \infty\} $ is a sequence of $ m $-widely acceptable ($ m $-WA) random variables, which is stochastically dominated by a random variable $ Y $ in sub-linear expectations space $ (\Omega, {\mathcal H}, \mathbb{E}) $, and $ \{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. A Rosenthal-type inequality for $ m $-WA random variables is also eatablished.
Fields of Study & Subjects
Probability and Risk Models
Stochastic processes and financial applications
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 5
- Pages
- 15215–15232
- Publication date
- 1 January 2026