Partially Observed Systems
We consider several problems of two-dimensional system identification when only one component of the system is observed. For linear diffusion-type processes, it is possible (using Kalman filtration) to construct the MLE and BE of unknown parameters and to describe their properties in regular (Section 6.1) and disorder (Section 6.3) cases. For nonlinear systems, calculation of the likelihood ratio is difficult, so we use some approximations of the original system and then apply the approach of a “misspecified model”. This allows us to construct pseudo-MLE’s and pseudo-BE’s and to prove their consistence and asymptotic normality (Section 6.2). We shall return to the identification of partially observed systems in Section 7.5, where we will use the minimum distance approach.
KeywordsKalman Filter Gaussian Process Wiener Process Asymptotic Normality Unobserved Component
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