On the Law of the Iterated Logarithm for m-dependent stationary random variables under sub-linear expectations

Wang-Yun Gu; Li-Xin Zhang

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arXiv · 2506.10522

On the Law of the Iterated Logarithm for m-dependent stationary random variables under sub-linear expectations

Wang-Yun Gu·Li-Xin Zhang

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Abstract

This paper explores the Law of the Iterated Logarithm (LIL) for $m$-dependent sequences under the framework of sub-linear expectations. We first extend existing LIL results to sequences of independent, non-identically distributed random variables under sub-linear expectations. This extension serves as a crucial intermediary step, facilitating the subsequent establishment of the LIL for $m$-dependent stationary sequences. On the other hand, we also establish necessary conditions for $m$-dependent sequences in sub-linear expectation spaces.

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BibTeX RIS

Wang-Yun Gu, Li-Xin Zhang. 2025-06-12. On the Law of the Iterated Logarithm for m-dependent stationary random variables under sub-linear expectations. https://arxiv.org/abs/2506.10522

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