Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic   Parabolic Equations with Additive Fractional Brownian Motion
  A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter $H\geq 1/2$.   The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation. 
Igor Cialenco, Sergey Lototsky, Jan Pospisil