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About: Zakai equation     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatStochasticDifferentialEquationsyago:WikicatStochasticProcessesyago:Abstraction100002137yago:Cognition100023271yago:Communication100033020yago:Concept105835747yago:Content105809192yago:DifferentialEquation106670521yago:Equation106669864yago:Hypothesis105888929yago:Idea105833840yago:MathematicalStatement106732169yago:Message106598915yago:Model105890249yago:PsychologicalFeature100023100yago:Statement106722453yago:StochasticProcess113561896 New Facet based on Instances of this Class

In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear stochastic partial differential equation for the normalized density of the hidden state. In principle either approach allows one to estimate a quantity function (the state of a dynamical system) from noisy measurements, even when the system is non-linear (thus generalizing the earlier results of Wiener and Kalman for linear systems and solving a central problem in estimation theory). The application of this approach to a specific engineering situation may be problematic however, as these equations are quite complex. The Zakai equation is a bilinear stochastic partial differential equation. It was na