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

As in Part I (see [I. A. Ibragimov and R. Z. Khas'minskii, Theory Probab. Appl., 43 (1999), pp. 370–387]), we consider the problem of estimation of functional parameters $a_k(t,x),\theta(t,x)$ by observing a solution $u_\varepsilon(t,x)$ of a stochastic partial differential equation
$$ du_\varepsilon(t)=\sum_{|k|\le 2p}a_kD_x^ku_\varepsilon+\theta\,dt+\varepsilon\,dw(t), $$
where $w(t)$ is a Wiener process. We investigate problems of the existence of consistent estimates for $\theta$ and their rate of convergence to $\theta$ dependent on properties of the functional class $\Theta$, which a priori contains $\theta$.