Related papers: Extreme Value Theory with Spectral Techniques: app…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
These notes are based on lectures delivered by G. Schehr at the XVIth School on Fundamental Problems in Statistical Physics (FPSP), held in Oropa (Italy) from 30 June to 11 July 2025. After a brief introduction to extreme value statistics…
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole. The presence of the latter influences the extremal index…
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 Fr\'echet (fat-tailed)…
In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional…
Periodic inspections are necessary to keep railroad tracks in state of good repair and prevent train accidents. Automatic track inspection using machine vision technology has become a very effective inspection tool. Because of its…
We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Extreme value theory (EVT) provides an elegant mathematical tool for the statistical analysis of rare events. When data are collected from multiple population subgroups, because some subgroups may have less data available for extreme value…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…
Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome.…
The classical multivariate extreme value theory tries to capture the extremal dependence between the components under a multivariate domain of attraction condition and it requires each of the components to be in the domain of attraction of…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
The classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…
Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and…