Spatio-temporal Ornstein-Uhlenbeck processes: theory, simulation and statistical inference

TL;DR

This paper develops the theoretical framework, simulation methods, and statistical inference techniques for spatio-temporal Ornstein-Uhlenbeck processes, demonstrating their practical application in radiation anomaly data analysis.

Contribution

It introduces a comprehensive approach to modeling, simulating, and inferring parameters for spatio-temporal Ornstein-Uhlenbeck processes, filling a gap in existing statistical methods.

Findings

Effective simulation strategies demonstrated

Application to radiation anomaly data shows practical relevance

Prediction methods outlined for Gaussian processes

Abstract

Spatio-temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio-temporal Ornstein-Uhlenbeck process. We conduct detailed simulation studies and demonstrate the practical relevance of these processes in an empirical study of radiation anomaly data. Finally, we describe how predictions can be carried out in the Gaussian setting.