Gaussian and Hermite Ornstein-Uhlenbeck processes

TL;DR

This paper investigates the long-term behavior of auto-covariance functions in Gaussian and Hermite Ornstein-Uhlenbeck processes, extending previous results to more general noise types and increment stationarity conditions.

Contribution

It generalizes existing asymptotic results for OU processes driven by Gaussian and Hermite noises, including non-stationary increment cases.

Findings

Derived asymptotic behaviors for auto-covariance functions.

Extended previous results to broader classes of Gaussian and Hermite noises.

Provided a unified framework for stationary and non-stationary increment cases.

Abstract

In the present paper we study the asymptotic behavior of the auto-covariance function for Ornstein-Uhlenbeck (OU) processes driven by Gaussian noises with stationary and non-stationary increments and for Hermite OU processes. Our results are generalizations of the corresponding results of Cheridito et al. \cite{CKM} and Kaarakka and Salminen \cite{KS}.