Year: 2026
Type: preprint
Abstract: We study a two-dimensional Ornstein-Uhlenbeck system where only the first coordinate is observed, whereas the second coordinate remains hidden. Our goal is the estimation of the coupling parameter in the drift of the observed coordinate. The core novelty lies in accounting for the influence of the observed component on the unobserved one, making the system fully coupled. Using linear filtering, we derive the likelihood under partial observation and establish local asymptotic normality of the statistical model. Within the Ibragimov-Hasminskii framework (1981), we prove consistency, asymptotic normality, convergence of moments and asymptotic efficiency of the MLE under stability and identifiability assumptions as the time horizon tends to infinity.
Source: arXiv (Cornell University)
Authors: Gaudlitz, Sascha, Gökalp, Hasan Mert
Institution: Humboldt-Universität zu Berlin
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7166707856
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