Identification of linear stochastic systems based on partial information (Q1897834)

The problem of identification of the matrices \(A\), \(\sigma\), \(H\), \(\sigma_0\) of a vector valued linear stochastic system \(dX(t)= AX(t) dt+ \sigma dW(t)\), \(X(0)= X_0\), \(dy(t)= HX(t) dt+ \sigma_0 dW_0\), \(y(0)= 0\) is formulated by a deterministic optimal control problem, where \(X\) is the state process and \(y\) describes the covariances of \(X_0\). The standard assumptions are fulfilled. A simulated annealing algorithm of the parameter estimation is constructed.