“…Theorems 3.7 and 4.7 do not give any rate of convergence, because of the use of Martingale convergence theorem, and it would be interesting to find finer methods that may give the rate of convergence, such as those [10,Section 4.3] available for the convergence of covariance of the filter for linear models. Further, partly because of the use of convergence of the smoother to prove filter stability, our results do not give much information about the structure of the asymptotic filtering distribution, such as that which is available [10,Sections 4.3,5], [37,Remark 3.2] for the linear filter. We hope that further investigations in this direction will lead to efficient numerical implementations of the filter for deterministic dynamics, especially for high dimensional systems.…”