A note on the central limit theorem for a one-sided reflected Ornstein-Uhlenbeck process

TL;DR

This paper establishes a functional central limit theorem for the idle process in a one-sided reflected Ornstein-Uhlenbeck process, providing theoretical insights into its long-term behavior.

Contribution

It introduces a new central limit theorem specifically for the idle process of a reflected Ornstein-Uhlenbeck process, extending existing stochastic process theory.

Findings

Proves a functional central limit theorem for the idle process

Characterizes the limiting distribution of the process

Enhances understanding of reflected Ornstein-Uhlenbeck dynamics

Abstract

In this short communication we present a (functional) central limit theorem for the idle process of a one-sided reflected Ornstein-Uhlenbeck proces.