On filtering equations in infinite dimensions (Q677475)

The authors consider a filtering problem in which the signal process evolves in an infinite-dimensional separable Hilbert space \(H\) while the observation process is in \(\mathbb{R}^d\). They establish the corresponding Zakai equation and give conditions under which the conditional probabilities are absolutely continuous with respect to a Gaussian reference measure in the Hilbert space \(H\). Both uncorrelated and correlated cases are treated. The main tool is the use of infinite-dimensional stochastic analysis.