Strong approximations in the almost sure central limit theorem and limit behavior of the center of mass

Zhishui Hu, Wei Wang and Liang Dong

Stochastic Processes and their Applications, 2025, vol. 182, issue C

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.

Keywords: Strong approximation; Almost sure central limit theorem; The center of mass; The law of the iterated logarithm; Step-reinforced random walk (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104570

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