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

• 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).

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

fractional Ornstein-Uhlenbeck processes

Malliavin calculus

Langevin equation

least-squares estimator

60G22

60H07

62F12

Statistics

statistik

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