The self-normalized Donsker theorem revisited
Probability
2017-10-31 v3
Abstract
We extend the Poincar\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space . This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\"{o}rg\H{o} et al. (2003). Some notes on spheres with respect to -norms are given.
Cite
@article{arxiv.1609.09283,
title = {The self-normalized Donsker theorem revisited},
author = {Peter Parczewski},
journal= {arXiv preprint arXiv:1609.09283},
year = {2017}
}
Comments
Published at http://dx.doi.org/10.15559/17-VMSTA82 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)