Note on the complete moment convergence of maximal partial sums for moving average process under sublinear expectations

Mingzhou Xu; Wei Wang; Mingzhou Xu; Wei Wang

doi:10.3934/math.2026539

AIMS Mathematics

2026, Volume 11, Issue 5: 13090-13109. doi: 10.3934/math.2026539

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Research article

Note on the complete moment convergence of maximal partial sums for moving average process under sublinear expectations

Mingzhou Xu ^,,
Wei Wang

School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen, 333403, China

Received: 28 February 2026 Revised: 20 April 2026 Accepted: 28 April 2026 Published: 11 May 2026
MSC : 60F05, 60F15

In this paper, the complete moment convergence for the maximal partial sums of moving average processes generated by $ \{Y_i, -\infty < i < \infty\} $ is proved under conditions that $ C_{ \mathbb{V}}\left(|Y_1|^p\left(1\vee l(f^{-1}(Y_1))\right)\right) < \infty $, where $ f^{-1} $ is the inverse function of $ f $, and $ \{Y_i, -\infty < i < \infty\} $ is a double sequence of identically distributed, negatively dependent random variables under sublinear expectations. The results established in sublinear expectation spaces complement and extend the corresponding ones in probability space in some extent.
- complete moment convergence,
- moving average processes,
- negatively dependent,
- sub-linear expectations
Citation: Mingzhou Xu, Wei Wang. Note on the complete moment convergence of maximal partial sums for moving average process under sublinear expectations[J]. AIMS Mathematics, 2026, 11(5): 13090-13109. doi: 10.3934/math.2026539

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Abstract

In this paper, the complete moment convergence for the maximal partial sums of moving average processes generated by $ \{Y_i, -\infty < i < \infty\} $ is proved under conditions that $ C_{ \mathbb{V}}\left(|Y_1|^p\left(1\vee l(f^{-1}(Y_1))\right)\right) < \infty $, where $ f^{-1} $ is the inverse function of $ f $, and $ \{Y_i, -\infty < i < \infty\} $ is a double sequence of identically distributed, negatively dependent random variables under sublinear expectations. The results established in sublinear expectation spaces complement and extend the corresponding ones in probability space in some extent.

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