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)
Subjects
Calculus of Variations and Optimal Control; Optimization
Control
Drift estimation
Ergodic processes
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Parameter estimation
Random noise
Simulation
Systems Theory
Theoretical
60G35
Parameter estimation
Multiple Wiener–Itô integrals
Strong consistency
Asymptotic normality
Ergodicity
60H07
Stochastic evolution equations
Malliavin calculus
Fractional Brownian motion
60H15
Fractional Ornstein–Uhlenbeck process
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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