On the Sieve Estimator for Fractional SPDEs from Discrete Observations

J.P.N. Bishwal

2023, v.29, Issue 3, 367-402


Consistency and asymptotic normality of the sieve
estimator of the drift coefficient of fractional stochastic partial differential equation
models using a finite number of Fourier coefficients 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 $H\ge 0.5$. Finally we study sieve estimation for interacting fractional diffusions.

Keywords: Stochastic partial differential equations, fractional Brownian motion, fractional Ornstein-Uhlenbeck process, discrete observations, mixingale limit theorems, long-memory, sieve method, approximate, functional data analysis, interacting fractional diffusions, fractional Curie-Weiss model, interacting fractional Black-Scholes models


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