An Estimation Problem for Quasilinear Stochastic Partial Differential Equations

A problem of estimating a functional parameter $\theta(x)$ and functionals $\Phi(\theta)$ based on observation of a solution $u_\varepsilon(t,x)$ of the stochastic partial differential equation
$$ du_\varepsilon(t)=\sum_{|k|\leq 2p}a_kD^k_xu_\varepsilon\,dt+\theta(x)g(u_\varepsilon,t,x) +\varepsilon\,dw(t) $$
is considered. The asymptotic problem setting, as the noise intensity $\varepsilon\to0$, is investigated.