Gaussian and Hermite Ornstein-Uhlenbeck processes

2021/06/23 by Es-Sebaiy, Khalifa
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2106.12311

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. \citeCKM and Kaarakka and Salminen \citeKS.

Related

• A Generalization of the Ornstein-Uhlenbeck Process: Theoretical Results, Simulations and Parameter Estimation
• Modeling stationary data by a class of generalised Ornstein-Uhlenbeck processes
• Ornstein-Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility
• On Ornstein-Uhlenbeck driven by Ornstein-Uhlenbeck processes
• Parameter estimation for an Ornstein-Uhlenbeck Process driven by a general Gaussian noise