@article{Siripraparat2024, 
author = {Tatpon Siripraparat and Suporn Jongpreechaharn},
title = {The exponential non-uniform bound on the half-normal approximation for the number of returns to the origin},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {19031-19048},
keywords = {half-normal approximation, the number of returns to the origin, Stein's method, symmetric simple random walk},
url = {https://www.sciopen.com/article/10.3934/math.2024926},
doi = {10.3934/math.2024926},
abstract = {This research explored the number of returns to the origin within the framework of a symmetric simple random walk. Our primary objective was to approximate the distribution of return events to the origin by utilizing the half-normal distribution, which is chosen for its appropriateness as a limit distribution for nonnegative values. Employing the Stein's method in conjunction with concentration inequalities, we derived an exponential non-uniform bound for the approximation error. This bound signifies a significant advancement in contrast to existing bounds, encompassing both the uniform bounds proposed by Döbler [1] and polynomial non-uniform bounds presented by Sama-ae, Chaidee, and Neammanee [2], and Siripraparat and Neammanee [3].}
}