This research provides insights into limiting behaviors in dependent models, suggesting implications for random walks.
We provide complementary results for a family of models with dependence on their previous k -sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass. Additionally, we explore the connection between our findings and the study of certain reinforced random walks in the literature.
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Vázquez-Guevara et al. (2026) studied this question.
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