Estimation for the damping factor of the driving process of an SPDE in two space dimensions

TL;DR

This paper develops a new method to estimate the damping factor in a two-dimensional SPDE driven by a Q-Wiener process, using high-frequency data and quadratic variations, with supporting simulation results.

Contribution

It introduces a novel estimator for the damping parameter of the driving process in a 2D SPDE based on quadratic variations, validated through simulations.

Findings

The estimator accurately recovers the damping parameter in simulated scenarios.

Simulation results demonstrate the estimator's effectiveness and robustness.

The method leverages high-frequency spatio-temporal data for parameter estimation.

Abstract

We study parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process based on high frequency spatio-temporal data. We give an estimator of the damping parameter of the $Q$-Wiener process of the SPDE based on quadratic variations with temporal and spatial increments. We also provide simulation results of the proposed estimator.