Parameter estimation for stochastic wave equation based on observation window

TL;DR

This paper develops and analyzes minimum contrast estimators for unknown parameters in a stochastic wave equation, demonstrating their consistency and normality through theoretical proofs and numerical simulations.

Contribution

It introduces new estimators for stochastic wave equations based on observed data, proving their statistical properties and applying them to Brownian noise perturbations.

Findings

Establishes strong consistency of the estimators.

Proves asymptotic normality of the estimators.

Validates results with numerical simulations.

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.