English

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

Probability 2012-07-11 v1

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\Z converges weakly to the arcsine distribution on [0,1][0,1].

Keywords

Cite

@article{arxiv.1207.2401,
  title  = {A rate of convergence for the arcsine law by Stein's method},
  author = {Christian Döbler},
  journal= {arXiv preprint arXiv:1207.2401},
  year   = {2012}
}