Statistical Inference for SPDEs: an overview

TL;DR

This paper reviews recent advances in statistical inference methods for parabolic SPDEs, focusing on spectral approaches and discrete sampling, highlighting key methodologies and open challenges.

Contribution

It provides a comprehensive overview of spectral and discrete sampling techniques for SPDEs, including recent developments and open problems.

Findings

Spectral approach is the most studied sampling scheme.

Discrete sampling of solutions is practically important.

Open problems in statistical inference for SPDEs are identified.

Abstract

The aim of this work is to give an overview of the recent developments in the area of statistical inference for parabolic stochastic partial differential equations. Significant part of the paper is devoted to the spectral approach, which is the most studied sampling scheme under which the observations are done in the Fourier space over some finite time interval. We also discuss into details the practically important case of discrete sampling of the solution. Other relevant methodologies and some open problems are briefly discussed over the course of the manuscript.