Drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process

Abstract

We analyze the least squares estimator for the drift parameter of an infinite-dimensional fractional Ornstein-Uhlenbeck process with Hurst parameter H >= 1/2 This estimator can be expressed in terms of a divergence integral with respect to the fractional Brownian motion. Using some recently developed criteria based on Malliavin calculus and Wiener-Ito chaos expansion, we prove the strong consistency and the asymptotic normality of the estimator. (C) 2013 Elsevier Masson SAS.

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Keywords

• Fractional Brownian motion
• Parameter estimation
• Stochastic evolution equations
• Malliavin calculus
• Multiple Wiener-Ito integrals
• Strong consistency
• Asymptotic normality