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

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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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Hua et al. (Thu,) studied this question.

synapsesocial.com/papers/68e616ccb6db6435875a98ea https://doi.org/https://doi.org/10.48550/arxiv.2407.03659

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