Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the second kind

作者：Azmoodeh Ehsan^*; Morlanes Jose Igor

来源：Statistics, 2015, 49(1): 1-18.

DOI：10.1080/02331888.2013.863888

• fractional Ornstein-Uhlenbeck processes
• Malliavin calculus
• Langevin equation
• least-squares estimator
• 60G22
• 60H07
• 62F12

The fractional Ornstein-Uhlenbeck process of the second kind (fOU(2)) is the solution of the Langevin equation with driving noise where B is a fractional Brownian motion with Hurst parameter H(0, 1). In this article, in the case H>1/2, we prove that the least-squares estimator introduced in [Hu Y, Nualart D. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Stat. Probab. Lett. 2010;80(11-12):1030-1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H(1/2, 1).

• 出版日期2015-1-2