Some Asymptotic Results of Gaussian Random Fields with Varying Mean   Functions and the Associated Processes
  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. 
Jingchen Liu and Gongjun Xu
math.ST math.PR stat.TH