A rate of convergence for the arcsine law by Stein's method

Christian Döbler

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arXiv · 1207.2401

A rate of convergence for the arcsine law by Stein's method

Christian Döbler

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Abstract

Using Stein's method for the Beta distributions and a recent technique by Goldstein and Reinert of comparing the Stein characterization of the target distribution with that of the approximating distribution we prove a rate of convergence in the classical arcsine law, which states that the distribution of the relative time spent positive by a symmetric random walk on $\Z$ converges weakly to the arcsine distribution on $[0,1]$.

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Christian Döbler. 2012-07-10. A rate of convergence for the arcsine law by Stein's method. https://arxiv.org/abs/1207.2401

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