(DEV) 🤖 VTeX: Solutions for Science Publishing

Keywords: Poincaré–Borel lemma

Journals

Title

Author

Types

Abstract

Keywords

Published

Pages

Volumes

Issues

DOI

Affiliation

Classifications

Search results 2

Order by:

Select: All None Download:

The self-normalized Donsker theorem revisited

Peter Parczewski

https://doi.org/10.15559/17-VMSTA82-T06281332

Pub. online: 18 Sep 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications

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

ℓ_{p}

-norms are given.

The self-normalized Donsker theorem revisited

Peter Parczewski

https://doi.org/10.15559/17-VMSTA82

Pub. online: 18 Sep 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications

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

ℓ_{p}

-norms are given.

Items per page

Detailed search

Search results 2

Export citation

Copy and paste formatted citation

Download citation in file

PDF Preview

Authors