One more approach to the convergence of the empirical process to the Brownian bridge

TL;DR

This paper offers a new, simplified proof of Donsker's theorem, demonstrating that the empirical process converges to the Brownian bridge, a fundamental result in probability theory.

Contribution

The paper introduces a novel, straightforward proof of the convergence of the empirical process to the Brownian bridge, enhancing understanding of this classical result.

Findings

Provides a simpler proof of Donsker's theorem

Confirms convergence of empirical process to Brownian bridge

Strengthens theoretical foundations of empirical process theory

Abstract

A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact.