Stability of the optimal filter in continuous time: Beyond the bene{\v   s} filter
  We are interested in the optimal filter in a continuous time setting. We want to show that the optimal filter is stable with respect to its initial condition. We reduce the problem to a discrete time setting and apply truncation techniques coming from [OR05]. Due to the continuous time setting, we need a new technique to solve the problem. In the end, we show that the forgetting rate is at least a power of the time t. The results can be re-used to prove the stability in time of a numerical approximation of the optimal filter. 
van Bien Bui (JAD), Sylvain Rubenthaler (JAD)
math.PR math.OC math.ST stat.TH