The stability of the nonlinear filter in continuous time.

Summary The filtering problem consists in estimating the state of a dynamic system, called a signal which is often a Markovian process, from noisy observations of past states of the system. In this paper, we consider a continuous time filtering model for the diffusion process. The goal is to study the stability of the optimal filter with respect to its initial condition beyond the (strong) mixing assumption for the transition kernel ignoring the ergodicity of the signal.