On asymptotic properties of the parameter estimator for a type of SPDE

In this paper, we study a random field Uɛ(t,x) governed by some type of stochastic partial differential equations with an unknown parameter θ and a small noise ɛ. We construct an estimator of θ based on the continuous observation of N Fourier coefficients of Uɛ(t,x), and prove the strong convergence and asymptotic normality of the estimator when the noise ɛ tends to zero.