On the sieve estimator for fractional SPDEs from discrete observations. (English) Zbl 07850865
The consistency and asymptotic normality of the sieve estimator of the drift coecient of fractional stochastic partial differential equation models using a fininite number of Fourier coeficients of the solution are studied based on observations at discrete times of a fixed time interval [0; T]. The equation is driven by additive noise that is white in space and color (fractional) in time with Hurst memory parameter H 0:5. Finally the author studies sieve estimation for interacting fractional diffusions.
Reviewer: Luis Vázquez (Madrid)
MSC:
| 35R11 | Fractional partial differential equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60F25 | \(L^p\)-limit theorems |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60G44 | Martingales with continuous parameter |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 62F12 | Asymptotic properties of parametric estimators |
| 62G05 | Nonparametric estimation |
| 62M07 | Non-Markovian processes: hypothesis testing |
| 62M09 | Non-Markovian processes: estimation |
