Abstracts for the PhD Course on Extremes in Space and Time, May 27-30 Extremes and sums of regularly varying observa- tions

s for the PhD Course on Extremes in Space and Time, May 27-30 Extremes and sums of regularly varying observations Bojan Basrak (University of Zagreb) In the first part, we show how the dependence structure of extremes in a stationary regularly varying sequence can be described, using the concept of the tail process. This is illustrated on some standard time series models. In the second part, we show how point process theory for extremes extends from iid to dependent sequences, aslong as their dependence vanishes when time goes on. We discuss appropriate formal conditions and show how they lead to various asymptotic results for such sequences. Due to the dependence, their extremes clusterasymptoticallyin a way which is captured by the corresponding tail process. Finally, we plan to discuss the convergence of sums for dependent regularly varying sequences and present some new functional limit theorems. Applications of Tail Dependence Dan Cooley (Colorado State University) We will present recent applications which require modeling the tail dependence of a random vector. In the first application, we aim to predict air pollution levels at an unobserved location given nearby measurements and given that the observed values are large. Specifically, we aim to estimate the conditional distribution of the pollution level at the unobserved location. We rely on the framework of regular variation to approximate the conditional distribution, given that the observed values are large. Using a fitted model for the angular measure of the regularvarying random vector, we apply our method to nitrogen dioxide measurements in metropolitan Washington DC. We show that our method is superior to standard linear prediction methods of approximating the conditional distribution when observed values are large. In the second application, we investigate the Pineapple Express phenomenon, a weather regime which can lead to extreme and destructive precipitation on North America’s Pacific Coast. Our first aim is to study climate models’ ability to reproduce these events. By applying bivariate extreme value theory, we measure the amount of tail dependence between the climate model output and observations. In an attempt to better understand and quantify the processes