CSDS seminar – Modelling of extreme excursions of stochastic processes in space and time: Foundations for a new tail process (Kirstin Strokorb)

Extreme excursions of stochastic processes in space and time often appear to be more localized the more extreme they are. While classical stochastic processes in extreme value theory cannot model this effect, we introduce an adapted version, where a suitable domain-scaling can be incorporated to accommodate this behaviour. Our theory is inspired by the triangular array convergence of maxima of Gaussian processes to a Brown–Resnick process and turns out to be natural in this context. We study key properties of the resulting tail process and demonstrate its ability to approximate conditional exceedance probabilities of a range of stochastic processes. Joint work with Marco Oesting and Raphael de Fondeville (based on the preprint https://publications.mfo.de/handle/mfo/4206).