Point Processes: Extreme Value Theory

This lecture covers the theory of point processes in the context of extreme value theory, focusing on the application of Poisson processes to model exceedances over thresholds. The instructor discusses the inefficiencies of the block maximum method and introduces alternative methods like peaks over thresholds and r-largest order statistics. The lecture explores the concept of a point process as a stochastic model for point patterns in a state space, emphasizing the importance of simplicity in the pattern. Additionally, the lecture delves into the visualization of point patterns, counting measures, Radon measures, and random measures. The application of point processes in modeling exceedances and the theoretical foundations of extreme value theory are highlighted.