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Half-normal approximation for statistics of symmetric simple random walk. (English) Zbl 1384.60064

Summary: In [“Stein’s method for the half-normal distribution with application to limit theorems related to simple random walk”, Preprint, arXiv:1303.4592], C. Döbler used Stein’s method to obtain the uniform bounds in half-normal approximation for three statistics of a symmetric simple random walk; the maximum value, the number of returns to the origin and the number of sign changes up to a given time \(n\). In this paper, we give the non-uniform bounds for these statistics by using Stein’s method and the concentration inequality approach.

MSC:

60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
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