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 a...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 81; no. 3; pp. 785 - 814
Main Authors Balde, Maoudo Faramba, Es-Sebaiy, Khalifa, Tudor, Ciprian A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2020
Springer Nature B.V
Springer Verlag (Germany)
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Summary: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-018-9519-4