Preprint arXiv:2307.06685 [math.PR]; last accessed July 30, 2023.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: Let X1,X2,... be the digits in the base-q expansion of a random variable X defined on [0,1) where q≥2 is an integer. For n=1,2,..., we study the probability distribution Pn of the (scaled) remainder ∑∞k=n+1Xqqn−k: If X has an absolutely continuous CDF then Pn converges in the total variation metric to Lebesgue measure on the unit interval; under certain smoothness conditions we establish exponentially fast convergence of Pn and its PDF fn; and we give examples of these results. The results are extended to the case of a multivariate random variable defined on a unit cube.
Bibtex:
@misc{,
title={How many digits are needed?},
author={Ira W. Herbst and Jesper Møller and Anne Marie Svane},
year={2023},
eprint={2307.06685},
archivePrefix={arXiv},
primaryClass={math.PR}
}
Reference Type: Preprint
Subject Area(s): Probability Theory