Gaussian Process: Covariance and Correlation Functions

This lecture covers the motivation behind extremal limit theorems, basic statistical analysis, and applications of point processes. It delves into Gaussian processes, covariance and correlation functions, intrinsic stationarity, Poisson process theory, and applications to extremes. The lecture also explores multivariate extremes and statistics, asymptotic estimating, and simulations. Various covariance and correlation functions are discussed, including isotropic, anisotropic, and nonstationary functions. The lecture concludes with examples of standard covariance functions and intrinsic stationarity in Gaussian processes.