Abstract

ABSTRACTIn 2013, Dƶbler used Steinā€™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 Steinā€™s method and the concentration inequality approach.

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