Strong Approximations in the Almost Sure Central Limit Theorem and Limit Behavior of the Center of Mass

Zhishui Hua; Wei Wanga; Liang Dong

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arXiv · 2407.03659

Strong Approximations in the Almost Sure Central Limit Theorem and Limit Behavior of the Center of Mass

Zhishui Hua·Wei Wanga·Liang Dong

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Abstract

In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a random sequence under a different strong approximation condition. Applications to step-reinforced random walks are also discussed.

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Zhishui Hua, Wei Wanga, Liang Dong. 2024-07-04. Strong Approximations in the Almost Sure Central Limit Theorem and Limit Behavior of the Center of Mass. https://arxiv.org/abs/2407.03659

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