Filtering Problems for Conditionally Linear Systems with Non-Gaussian Initial Conditions

Abstract

We solve the filtering problems for conditionally linear systems, that is, stochastic, partially observable systems which are linear in unobservable processes and nonlinear in observable processes, with non-Gaussian initial conditions. We assume that all coefficients of given SDEs are Lipshitz continuous in the observable processes, and that certain quantities concerning the diffusion coefficients of given SDEs are uniformly nonsingular. But we assume nothing about the initial distribution and allow that a part of the coefficients of the given SDEs are of linear growth order in the observable processes.