Applied Mathematics and Optimization, Vol.81, No.3, 785-814, 2020
Ergodicity and Drift Parameter Estimation for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process of the Second Kind
We introduce the Hilbert-valued fractional Ornstein-Uhlenbeck of the second kind as the mild solution of a stochastic evolution equation with fractional-type Gaussian noise. We study the stationarity and the ergodicity for this infinite-dimensional process. Finally, via Malliavin calculus, we also analyze the least squares estimator of the drift parameter of the fractional Ornstein-Uhlenbeck of the second kind.