Gaussian and hermite Ornstein–Uhlenbeck processes

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. and Kaarakka and Salminen.

Keywords:

• Gaussian and Hermite Ornstein–Uhlenbeck processes
• auto-covariance function
• stationarity and ergodicity

MATHEMATICS SUBJECT CLASSIFICATIONS 2020:

• Primary 60H10
• Secondary: 60G15
• 60G10
• 60G22

Acknowledgments

I thank the two anonymous reviewers for their helpful comments and suggestions.

Additional information

Funding

This project was funded by Kuwait Foundation for the Advancement of Sciences (KFAS) under project code: PR18-16SM-04.