On the convergence of degenerate risk sensitive filters

We propose a degenerate risk sensitive filter which is an extension of the risk sensitive filtering paradigm to the case in which the evolution of the covariance matrix of the prediction error can be singular. We show that the corresponding risk sensitive Riccati iteration, describing the evolution of the covariance matrix of the prediction error, converges if the risk sensitivity parameter and the eigenvalues of the initial covariance matrix are sufficiently small.