An identification problem for partially observed infinite dimensional linear stochastic systems

Abstract

In the paper an identification problem is considered for partially observed autonomous infinite dimensional stochastic systems with additive noise. This state equation is described by an infinite dimensional linear Itô equation with additive Gaussian noise.The observations of the states are finite dimensional

We formulate the identification problem as an deterministic optimization problem with appropriate objective functionals for finite and infinite time horizons in such a way so that estimations of the system parameters and the covariance operators of the noise processes can be determined. The existence of these estimations is proved and a finite dimensional approximation is given

Keywords:

• Identification
• Optimization
• Partially Observed
• Inlinite Dimensional Stochastic Systems