Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations

Mingzhou Xu; Mingzhou Xu

doi:10.3934/math.2023871

AIMS Mathematics

2023, Volume 8, Issue 7: 17067-17080. doi: 10.3934/math.2023871

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Research article

Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations

Mingzhou Xu ^,

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

Received: 28 March 2023 Revised: 08 May 2023 Accepted: 08 May 2023 Published: 17 May 2023
MSC : 60F15, 60F05

Suppose that $ \{a_i, -\infty < i < \infty\} $ is an absolutely summable set of real numbers, $ \{Y_i, -\infty < i < \infty\} $ is a subset of identically distributed, negatively dependent random variables under sub-linear expectations. Here, we get complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of moving average processes $ \{X_n = \sum_{i = -\infty}^{\infty}a_{i}Y_{i+n}, n\ge 1\} $ produced by $ \{Y_i, -\infty < i < \infty\} $ of identically distributed, negatively dependent random variables under sub-linear expectations, complementing the relevant results in probability space.
- complete moment convergence,
- complete convergence,
- negatively dependent random variables,
- sub-linear expectations
Citation: Mingzhou Xu. Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations[J]. AIMS Mathematics, 2023, 8(7): 17067-17080. doi: 10.3934/math.2023871

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Abstract

Suppose that $ \{a_i, -\infty < i < \infty\} $ is an absolutely summable set of real numbers, $ \{Y_i, -\infty < i < \infty\} $ is a subset of identically distributed, negatively dependent random variables under sub-linear expectations. Here, we get complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of moving average processes $ \{X_n = \sum_{i = -\infty}^{\infty}a_{i}Y_{i+n}, n\ge 1\} $ produced by $ \{Y_i, -\infty < i < \infty\} $ of identically distributed, negatively dependent random variables under sub-linear expectations, complementing the relevant results in probability space.

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