Moderate deviation principle for $ m $-dependent random variables under the sub-linear expectation

Shuang Guo; Yong Zhang; Shuang Guo; Yong Zhang

doi:10.3934/math.2022331

AIMS Mathematics

2022, Volume 7, Issue 4: 5943-5956. doi: 10.3934/math.2022331

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Research article

Moderate deviation principle for $ m $-dependent random variables under the sub-linear expectation

Shuang Guo ,
Yong Zhang ^,

School of mathematics, Jilin University, Changchun 130012, China

Received: 10 November 2021 Revised: 29 December 2021 Accepted: 06 January 2022 Published: 13 January 2022
MSC : 60F10

Let $ \{X_n, n\geq1\} $ be a sequence of $ m $-dependent strictly stationary random variables in a sub-linear expectation $ (\Omega, \mathcal{H}, \mathbb{E}) $. In this article, we give the definition of $ m $-dependent sequence of random variables under sub-linear expectation spaces taking values in $ \mathbb{R} $. Then we establish moderate deviation principle for this kind of sequence which is strictly stationary. The results in this paper generalize the result that in the case of independent identically distributed samples. It provides a basis to discuss the moderate deviation principle for other types of dependent sequences.
- moderate deviation principle,
- $ m $-dependent random variables,
- sub-linear expectation,
- stationary sequences
Citation: Shuang Guo, Yong Zhang. Moderate deviation principle for $ m $-dependent random variables under the sub-linear expectation[J]. AIMS Mathematics, 2022, 7(4): 5943-5956. doi: 10.3934/math.2022331

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Abstract

Let $ \{X_n, n\geq1\} $ be a sequence of $ m $-dependent strictly stationary random variables in a sub-linear expectation $ (\Omega, \mathcal{H}, \mathbb{E}) $. In this article, we give the definition of $ m $-dependent sequence of random variables under sub-linear expectation spaces taking values in $ \mathbb{R} $. Then we establish moderate deviation principle for this kind of sequence which is strictly stationary. The results in this paper generalize the result that in the case of independent identically distributed samples. It provides a basis to discuss the moderate deviation principle for other types of dependent sequences.

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