Some Asymptotic Results of Gaussian Random Fields with Varying Mean Functions and the Associated Processes

TL;DR

This paper derives tail approximations for integrals of exponential Gaussian random fields with varying means, aiding applications in spatial hypothesis testing, Bayesian analysis, and finance.

Contribution

It provides new asymptotic results for Gaussian fields with non-constant means, extending existing theories to more complex models.

Findings

Derived tail approximations for integrals of Gaussian fields

Provided approximations for associated point processes

Applied results to spatial, Bayesian, and financial models

Abstract

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple applications such as hypothesis testing for spatial models, study of the distribution of Bayesian marginal likelihood and Bayes factor, and financial applications.