On the Stability of Kalman--Bucy Diffusion Processes
On the Stability of Kalman--Bucy Diffusion Processes
The Kalman--Bucy filter is the optimal state estimator for an Ornstein--Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional exact implementation of the optimal Bayes filter. It is generally the only such finite-dimensional exact instance of the …