Runs of Extremes of Observables on Dynamical Systems and Applications

2023/11/06 by Carney, Meagan, Holland, Mark, Nicol, Matthew +1 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2311.02864

Abstract

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fréchet (fat-tailed) or Weibull (bounded) distribution. The motivation for this work was to give estimates of the probabilities of sustained periods of weather anomalies such as heat-waves, cold spells or prolonged periods of rainfall in climate models. Our predictions are borne out by numerical simulations and also analysis of rainfall and temperature data.

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• A novel statistical workflow for nonstationary modelling of successive Fréchet extremes

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