ABSTRACT
The state of the system satisfies a vector valued sde driven by weak vector valued standard Brownian motion. The measurement process at any given time is a function of the state plus measurement noise. The desired trajectory satisfies the same differential equation as the state process but without process noise. The perturbing Hamiltonian is small and this smallness is characterized by a perturbation parameter. Using standard quantum mechanical time dependent perturbation theory or equivalently, the Dyson series expansion, the problem is to calculate the probability of the system making transition from one stationary state of the unperturbed system to another in terms of the perturbation parameter. This rate functional is used to calculate the approximate probability for the error to deviate from zero by an amount greater than a given threshold and the parameters of the system including the Gain matrix in the feedback term are adjusted for this deviation probability to be minimized.
