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

作者：Maslowski Bohdan^*; Tudor Ciprian A

来源：Bulletin des Sciences Mathematiques, 2013, 137(7): 880-901.

DOI：10.1016/j.bulsci.2013.04.008

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

We analyze the least squares estimator for the drift parameter of an infinite-dimensional fractional Ornstein-Uhlenbeck process with Hurst parameter H %26gt;= 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.

• 出版日期2013-11