Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises
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Abstract
We consider the filtering problem for partially observable stochastic processes solutions to systems of stochastic difference equations. In the first part of the paper we shall present a simple constructive method to obtain finite dimensional filters in discrete time. Then, applying some well-known results, mainly on the product of independent positive random variables, we shall present new finite dimensional filters and interpret some known results in a more general setting.Stochastic filtering Finite dimensional filters