Approximate and limit results for nonlinear filters with small observation noise: the linear sensor and constant diffusion coefficient case

Recursive approximations for a class of filtering problems are presented. This class is characterized by linear observation sensor, constant diffusion terms, and, for the multidimensional problem, potential-like conditions on the drift. For the case of small observation noise, these approximations are used to demonstrate the Gaussian limiting structure of the optimal nonlinear filter.<
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