On estimation of time dependent spatial signal in Gaussian white noise

We consider an estimation problem for time dependent spatial signal observed in a presence of additive cylindrical Gaussian white noise of a small intensity ε. Under known a priori smoothness of the signal estimators with asymptotically the best in the mimimax sense risk convergence rate in ε to zero are proposed. Moreover, on-line estimators for the signal and its derivatives in t are also created.