Year: 2024
Type: preprint
Abstract: The coefficients of elastic and dissipative operators in a linear hyperbolic SPDE are jointly estimated using multiple spatially localised measurements. As the resolution level of the observations tends to zero, we establish the asymptotic normality of an augmented maximum likelihood estimator. The rate of convergence for the dissipative coefficients matches rates in related parabolic problems, whereas the rate for the elastic parameters also depends on the magnitude of the damping. The analysis of the observed Fisher information matrix relies upon the asymptotic behaviour of rescaled $M, N$-functions generalising the operator cosine and sine families appearing in the undamped wave equation. In contrast to the energetically stable undamped wave equation, the $M, N$-functions emerging within the covariance structure of the local measurements have additional smoothing properties similar to the heat kernel, and their asymptotic behaviour is analysed using functional calculus.
Source: arXiv (Cornell University)
Authors: Tiepner, Anton, Ziebell, Eric
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4402345272