Estimation problems for coefficients of stochastic partial differential equations. Part III

This paper is concerned with the problem of estimating a functional parameter $a_0(t,x)$ upon observation of a solution $u_\varepsilon(t,x)$ of the stochastic partial differential equation
$$ du_\varepsilon(t)=\sum_{|k|\le 2p}a_kD_x^ku_\varepsilon\,dt+f\,dt+\varepsilon\,dw(t)=0. $$
Asymptotically minimax estimates for $a_0$ and asymptotically effective estimates for $\Phi(a_0)$ are found under the assumption that $a_0$ is independent of $t$.