Related papers: Extremes of regularly varying stochastic volatilit…
Extreme events are often multivariate in nature. A compound extreme occurs when a combination of variables jointly produces a significant impact, even if individual components are not necessarily marginally extreme. Compound extremes have…
We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator…
In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes $(Z_n(f))_{f\in\mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of…
To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended…
Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L\'evy processes provide a natural mathematical framework for…
The conditional extremes (CE) framework has proven useful for analysing the joint tail behaviour of random vectors. However, when applied across many locations or variables, it can be difficult to interpret or compare the resulting extremal…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
When there is no independence, abnormal observations may have a tendency to appear in clusters instead of scattered along the time frame. Identifying clusters and estimating their size are important problems arising in statistics of…
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying…
To address the need for efficient inference for a range of hydrological extreme value problems, spatial pooling of information is the standard approach for marginal tail estimation. We propose the first extreme value spatial clustering…
We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…
In a previous paper, the authors proved a conjecture of Lalley and Sellke that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a Gumbel distribution. The result is…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
We consider a stationary regularly varying time series which can be expressedas a function of a geometrically ergodic Markov chain. We obtain practical conditionsfor the weak convergence of the tail array sums and feasible estimators…
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process:…
We consider a last progeny modified branching random walk, in which the position of each particle at the last generation $n$ is modified by an i.i.d. copy of a random variable $Y$. Depending on the asymptotic properties of the tail of $Y$,…