Estimating Speed and Damping in the Stochastic Wave Equation
W. Liu, S. V. Lototsky
TL;DR
This paper develops a spectral estimator for the speed and damping parameters in a stochastic wave equation driven by Gaussian noise, analyzing its asymptotic behavior as the number of Fourier coefficients grows.
Contribution
It introduces a spectral estimation method for stochastic wave equations and studies its asymptotic properties with increasing Fourier coefficients.
Findings
Estimator's asymptotic normality established
Consistent estimation as Fourier modes increase
Applicable for fixed observation time and noise level
Abstract
A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier coefficients of the solution. The asymptotic properties of the estimator are studied as the number of the Fourier coefficients increases, while the observation time and the noise intensity are fixed.
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Taxonomy
TopicsStochastic processes and financial applications · Probabilistic and Robust Engineering Design · Meteorological Phenomena and Simulations