Conditionally Gaussian Processes

Abstract

Let (θ, ξ) = (θ _t , ξ _t ), 0 ≤ t ≤ T, be a random process with unobservable first component and observable second component. In employing the equations of optimal nonlinear filtering given by (8.10) one encounters an essential difficulty: in order to find π _t (θ), it is necessary to know the conditional moments of the higher orders

$${{\pi }_{t}}\left( {{{\theta }^{2}}} \right) = M\left( {\theta _{t}^{2}\left| {\mathcal{F}_{t}^{\xi }} \right.} \right),{{\pi }_{t}} = \left( {{{\theta }^{3}}} \right) = M\left( {\theta _{t}^{3}\left| {\mathcal{F}_{t}^{\xi }} \right.} \right)$$

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