Statistical Approach to Dynamical Inverse Problems

Based on nonparametric estimation ideas, a statistical approach to the dynamical inverse problem for some n ^th order nonlinear differential equations is introduced. It is proved that the real-time filter type of estimators converge respectively, as the data noise tends to zero, to the unknown force function and its derivatives at an optimal rate in the minimax sense. Received: 10 October 1996 / Accepted: 20 January 1997