# Construction of a relativistic Ornstein-Uhlenbeck process

## TL;DR

This paper constructs a relativistic Ornstein-Uhlenbeck process using a modified Dudley's Wiener process on the mass shell, and computes its invariant distribution and related processes.

## Contribution

It introduces a novel relativistic Ornstein-Uhlenbeck process model based on Dudley's Wiener process and derives its invariant distribution.

## Key findings

- Invariant distribution of the process computed
- Model extends classical Ornstein-Uhlenbeck to relativistic context
- Provides analytical tools for relativistic stochastic processes

## Abstract

Based on a version of Dudley's Wiener process on the mass shell in the momentum Minkowski space of a massive point particle, a model of a relativistic Ornstein--Uhlenbeck process is constructed by addition of a specific drift term. The invariant distribution of this momentum process as well as other associated processes are computed.