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⩾12. 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–Itô chaos expansion, we prove the strong consistency and the asymptotic normality of the estimator.