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

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 $\mathbb{Z}$ converges weakly to the arcsine distribution on $[0,1]$.

References in corpus (3)

• Exponential Approximation by Stein's Method and Spectral Graph Theory
• Stein's method of exchangeable pairs for absolutely continuous, univariate distributions with applications to the Polya urn model
• Discrete Stein characterizations and discrete information distances

Cited by in corpus (3)

• Stein's method for the half-normal distribution with applications to limit theorems related to the simple symmetric random walk
• Dirichlet approximation of equilibrium distributions in Cannings models with mutation
• Arcsine laws for random walks generated from random permutations with applications to genomics