The self-normalized Donsker theorem revisited

DOI10.15559/17-VMSTA82zbMath1378.60053arXiv1609.09283MaRDI QIDQ1686349

Peter Parczewski

Publication date: 22 December 2017

Published in: Modern Stochastics. Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.09283

zbMATH Keywords

Brownian motionself-normalized sumsDonsker theoremPoincaré-Borel lemma

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Cites Work

• Unnamed Item
• Unnamed Item
• Approximate independence of distributions on spheres and their stability properties
• A dozen de Finetti-style results in search of a theory
• When is the Student \(t\)-statistic asymptotically standard normal?
• Donsker's theorem for self-normalized partial sums processes
• Invariance principles for adaptive self-normalized partial sums processes.
• Projecting the surface measure of the sphere of \({\ell}_p^n\)
• The Wiener sphere and Wiener measure
• Does there exist a Lebesgue measure in the infinite-dimensional space?
• Stochastic calculus for fractional Brownian motion and related processes.
• Geometry of differential space
• Statistical analysis on high-dimensional spheres and shape spaces
• Lectures on Gaussian Processes
• On the Volume of the Intersection of Two L n p Balls
• Self-Normalized Processes
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Weak Convergence of Self-normalized Partial Sums Processes
• A Fractional Donsker Theorem

This page was built for publication: The self-normalized Donsker theorem revisited