Vit Kubelka, Bohdan Maslowski
Published 2019-03-27Version 1
Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to linear SPDEs driven by Gauss-Volterra process observed at finitely many points of the domain.
The LIL for $U$-statistics in Hilbert spaces
The order of convergence in the averaging principle for slow-fast systems of SDE's in Hilbert spaces
Large deviation for diffusions and Hamilton--Jacobi equation in Hilbert spaces
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