# Weak Convergence of Stationary Empirical Processes

## TL;DR

This paper extends the weak convergence results of empirical processes to more general, function-indexed processes under broad dependence conditions, providing a unified framework for stationary empirical processes.

## Contribution

It introduces a general weak convergence result for empirical processes indexed by functions of bounded variation, applicable under alpha mixing dependence.

## Key findings

- Weak convergence established for processes indexed by functions of bounded variation.
- Applicable to stationary sequences with alpha mixing dependence.
- Extends classical empirical process results to more general settings.

## Abstract

We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of dependence of the underlying sequence of random variables. As a consequence we establish weak convergence for stationary empirical processes indexed by general classes of functions under alpha mixing conditions.