A Powerful Numerical Technique Solving Zakai Equation for Nonlinear Filtering

In this paper we have developed a simple but powerful numerical method forthe approximation of the unnormalized conditional (probability) density offiltered diffusion process which satisfies Zakai equation and solves thenonlinear filtering problem. Using Galerkin technique the solution of Zakaiequation is approximated by means of a sequence of nonstandard basisfunctions given by a parameterized family of Gaussian densities. The methodis then illustrated by some examples.

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