2025/04/03 by Zhishui Hu, Hu, Zhishui · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #DNA and Biological Computing #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2504.02502
openalex publication_date 2025/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study both the positively and negatively step-reinforced random walks with parameter p. For a step distribution μ with finite second moment, the positively step-reinforced random walk with p∈ [1/2,1) and the negatively step-reinforced random walk with p∈ (0,1) converge to a normal distribution under suitable normalization. In this work, we obtain the rates of convergence to normality for both cases under the assumption that μ has a finite third moment. In the proofs, we establish a Berry-Esseen bound for general functionals of independent random variables, utilize the randomly weighted sum representations of step-reinforced random walks, and apply special comparison arguments to quantify the Kolmogorov distance between a mixed normal distribution and its corresponding normal distribution.