The self-normalized Donsker theorem revisited
Volume 4, Issue 3 (2017), pp. 189–198
Pub. online: 18 September 2017
Type: Research Article
Open Access
Open Access
Received
18 May 2017
18 May 2017
Revised
9 August 2017
9 August 2017
Accepted
9 August 2017
9 August 2017
Published
18 September 2017
18 September 2017
Abstract
We extend the Poincaré–Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Csörgő et al. (2003). Some notes on spheres with respect to $\ell _{p}$-norms are given.
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