# On the Simulation of General Tempered Stable Ornstein-Uhlenbeck Processes

## TL;DR

This paper provides an explicit transition law for tempered stable Ornstein-Uhlenbeck processes and introduces an exact simulation method applicable to broad classes of univariate and multivariate distributions.

## Contribution

It offers a novel explicit representation for the transition law and a rejection sampling algorithm for exact simulation of these processes.

## Key findings

- Explicit transition law derived for tempered stable Ornstein-Uhlenbeck processes
- Rejection sampling algorithm developed for exact simulation
- Results encompass many previously studied cases as special instances

## Abstract

We give an explicit representation for the transition law of a tempered stable Ornstein-Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation of increments from this process. Our results apply to general classes of both univariate and multivariate tempered stable distributions and contain a number of previously studied results as special cases.