Multivariate and spatial extremes for the analysis of air quality data

In recent years statistical analyses for monitoring the environment are increasingly in demand in di erent areas such as epidemiology, engineering, economy, etc. An example is the statistical monitoring of air quality, which makes it possible to statistically quantify the amount of certain pollutants in the lower troposphere. For a better understanding of the stochastic behavior of pollutants we focus on describing their extreme responses, because excessively extreme levels in the air may have implications in the environment and on human health. We then consider multivariate extreme value models and the class of maxstable processes in order to asses the frequencies of several extreme pollutant levels in central Europe and their spatial dependence structure.