Point Processes: Convergence and Gaussian Processes

This lecture introduces point processes as stochastic models for point patterns in a state space, discussing counting measures, Radon measures, and random measures. It covers the convergence of point processes and Laplace functionals, establishing weak convergence criteria. Additionally, it explores Gaussian processes, focusing on covariance and correlation functions, isotropic and anisotropic covariance, and constructing new correlation functions. The lecture concludes with simulations of Gaussian processes and intrinsic stationarity, defining stationary processes and semivariograms.