Estimation Theory for Abstract Evolution Equations Excited by General White Noise Processes

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Abstract
The filtering smoothing and prediction problems are solved for a general class of linear infinite-dimensional systems. The dynamical system is modeled as an abstract evolution equation, which includes linear ordinary differential equations, classes of linear partial differential equations and linear differential delay equations. The noise process is modeled using a stochastic integral with respect to a class of Hilbert space-valued stochastic processes, which includes the Wiener process and the Poisson process as special cases. The observation process is finite-dimensional and is corrupted by Gaussian-type white noise, which is modeled using the Wiener integral. The theory is illustrated by an application to an environmental problem.

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