Parameter estimation for stochastic wave equation based on observation window

Abstract

Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong consistency and asymptotic normality is proved. The results are applied to stochastic wave equation perturbed by Brownian noise and they are illustrated by a numerical simulation.

36 pages, 18 figures. arXiv admin note: text overlap with arXiv:1806.04045