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

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.

38 pages and 2 figures

References in corpus (5)

• Validity of the expected Euler characteristic heuristic
• Topology of structure in the Sloan Digital Sky Survey: model testing
• High level excursion set geometry for non-Gaussian infinitely divisible random fields
• Tail approximations of integrals of Gaussian random fields
• The distribution of maxima of approximately Gaussian random fields