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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 $[0,1]$.
An introduction to probability theory and its applications. Vol. I
William Feller · 1968
Earlier work this paper cites.
A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
Charles Stein · 1972
Earlier work this paper cites.
Poisson approximation for dependent trials
Louis H. Y. Chen · 1975
Earlier work this paper cites.
Stein’s method for the Gamma distribution and related statistical applications
Ho Ming Luk · 1994
Earlier work this paper cites.
Use of exchangeable pairs in the analysis of simulations
Charles Stein, Persi Diaconis, Susan Holmes, and Gesine Reinert · 2004
Cited alongside, same era.
Stein’s method for dependent random variables occurring in statistical mechanics
Peter Eichelsbacher and Matthias Löwe · 2010
Cited alongside, same era.
Exponential approximation by Stein’s method and spectral graph theory
Sourav Chatterjee, Jason Fulman, and Adrian Röllin · 2011
Cited alongside, same era.
Normal approximation by Stein’s method
Louis H. Y. Chen, Larry Goldstein, and Qi-Man Shao · 2011
Cited alongside, same era.
Discrete Stein characterizations and discrete information distances
C. Ley and Y. Swan
Cited in the paper.
Total variation error bounds for geometric approximation
Erol Peköz, Adrian Röllin, and Nathan Ross
Cited in the paper.
Nonnormal approximation by Stein’s method of exchangeable pairs with application to the Curie-Weiss model
Sourav Chatterjee and Qi-Man Shao · 2011
Later among the works it cites.
New rates for exponential approximation and the theorems of Rényi and Yaglom
Erol A. Peköz and Adrian Röllin · 2011
Later among the works it cites.
C. Döbler · 2012
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Stein’s method for the Beta distribution and the Polyà-Eggenberger Urn
L. Goldstein and G. Reinert · 2012
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