Asymptotic study of estimation problems with small observation noise

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Abstract

In this paper, we study the nonlinear filtering of multidimensional diffusions which are measured in a low noise channel. We describe approximate filters which are solutions of stochastic differential equations driven by the observation process; upper bounds for the corresponding approximation errors are given. The proof is detailed in a particular case where the result can be improved; in particular, the efficiency of the extended Kalman filter is studied.