Abstract
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.
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