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Robust diffusion approximation for nonlinear filtering

In this paper, we consider the filtering of diffusion processes observed in non-Gaussian noise, when diffusion approximations for the system apply. Standard continuity results show then that the filtering error using the optimal filter for the limit model is close to the error for the limit system. However, this procedure is known to be in general suboptimal. We show that for a certain class of models where the observation is in discrete time and corrupted by i.i.d. (non Gaussian) noise, a pointwise pre-processing is enough to recover optimality. This strengthens some recent results of Goggin. We further exhibit the role of the “signal-to-noise” ratio in the analysis of the performance of the system, and prove monotonicity (in this ratio) of the filtering error. Finally, we provide a filtering lower bound for a class of wide bandwidth observation processes.