A PROBLEM IN STOCHASTIC AVERAGING OF NONLINEAR FILTERS

We consider the stochastic averaging of a particular degenerate problem in nonlinear filtering. In particular, we consider a problem on the cylinder with fast angular diffusion and slow axial diffusion. The observation process depends only on the fast angle. We show that as the separation of scales (between fast and slow) grows, one can approximate the filter for the original problem by a much simpler one. Although our problem is similar to a number of others considered in the literature, the techniques required are different from the known ones.

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