Efficient Simulation of $p$-Tempered $\alpha$-Stable OU Processes

TL;DR

This paper introduces efficient simulation techniques for p-tempered alpha-stable Ornstein-Uhlenbeck processes applicable in univariate and multivariate contexts, with explicit transition law representations and practical validation.

Contribution

It provides novel simulation methods for p-tempered alpha-stable OU processes, including explicit transition law formulas for the background driving Lévy process.

Findings

Methods perform well in practical simulations

Explicit transition law derived for general p and alpha

Applicable to both univariate and multivariate cases

Abstract

We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $\alpha$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider both the case where the $\ts$ distribution is the stationary law and where it is the distribution of the background driving L\'evy process (BDLP). In the latter case, we also derive an explicit representation for the transition law as this was previous known only in certain special cases and only for $p=1$ and $\alpha\in[0,1)$. Simulation results suggest that our methods work well in practice.