Parameter estimation for stochastic partial differential equations of second order

TL;DR

This paper develops and analyzes minimum contrast estimators for second-order stochastic partial differential equations with two unknown parameters, demonstrating their consistency and asymptotic normality, with applications to hyperbolic equations with Brownian noise.

Contribution

Introduces new minimum contrast estimators for second-order SPDEs, proving their strong consistency and asymptotic normality, and applies results to hyperbolic equations with stochastic perturbations.

Findings

Establishes strong consistency of the estimators.

Proves asymptotic normality of the estimators.

Applies the methodology to hyperbolic equations with Brownian noise.

Abstract

Stochastic partial differential equations of second order with two unknown parameters are studied. Based on ergodicity, two suitable families of minimum constrast estimators are introduced. Strong consistency and asymptotic normality of estimators are proved. The results are applied to hyperbolic equations perturbed by Brownian noise.