Discrete - time risk - sensitive lters with non - Gaussianinitial conditions and their ergodic

In this paper, we study asymptotic stability properties of risk-sensitive lters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risk-sensitive lter asymptotically converges to any suboptimal lter initialized with an incorrect covariance matrix for the initial state vector in the mean square sense provided the incorrect initializing value for the covariance matrix results in a risk-sensitive lter that is asymptotically stable. For non-Gaussian initial conditions, we show that under certain conditions, a suboptimal risk-sensitive lter initialized with Gaussian initial conditions asymptotically approaches the optimal risk-sensitive lter for non-Gaussian initial conditions in the mean square sense.