Small dispersion asymptotics for an SPDE in two space dimensions using triple increments

TL;DR

This paper develops estimators for parameters in a 2D linear parabolic SPDE driven by small noise, using high-frequency data and increment-based methods, with simulation validation.

Contribution

It introduces novel estimators for diffusive, advective, and reaction parameters in a 2D SPDE using high-frequency data and increment techniques.

Findings

Consistent estimators for diffusive and advective parameters.

An estimator for the reaction parameter based on coordinate process approximation.

Simulation results demonstrating estimator performance.

Abstract

We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process with a small noise based on high frequency spatio-temporal data. We first provide estimators of the diffusive and advective parameters in the SPDE using temporal and spatial increments. We then construct an estimator of the reaction parameter in the SPDE based on an approximate coordinate process. We also give simulation results of the proposed estimators.