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This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…

Methodology · Statistics 2017-12-19 Ragnhild C. Noven , Almut E. D. Veraart , Axel Gandy

For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…

Probability · Mathematics 2019-05-06 Cees de Valk , Johan Segers

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

Statistics Theory · Mathematics 2025-06-03 Sibsankar Singha , Marie Kratz , Sreekar Vadlamani

We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the…

Probability · Mathematics 2013-05-09 Andrey Sarantsev

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)…

Dynamical Systems · Mathematics 2023-11-07 Meagan Carney , Mark Holland , Matthew Nicol , Phuong Tran

We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…

Dynamical Systems · Mathematics 2017-06-27 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Sandro Vaienti

We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…

Dynamical Systems · Mathematics 2025-06-04 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Mike Todd

This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…

Probability · Mathematics 2026-05-29 Shuyang Bai , Marie-Christine Duker

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…

Statistics Theory · Mathematics 2018-07-18 Hanan Ahmed , John H. J. Einmahl

A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…

Quantum Physics · Physics 2026-05-26 Partha Ghose

The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the…

Probability · Mathematics 2016-04-07 Ioannis Papastathopoulos , Kirstin Strokorb , Jonathan A. Tawn , Adam Butler

The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…

Methodology · Statistics 2013-10-02 Danijel Grahovac , Mofei Jia , Nikolai N. Leonenko , Emanuele Taufer

We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…

Probability · Mathematics 2025-06-25 Bojan Basrak , Ilya Molchanov , Hrvoje Planinić

This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…

Probability · Mathematics 2025-05-27 Zhangting Chen , Bingjie Wang , Dongya Cheng

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

Statistical Mechanics · Physics 2013-07-01 George W A Constable , Alan J McKane , Tim Rogers

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

Statistical Mechanics · Physics 2014-06-03 Joseph D. Challenger , Duccio Fanelli , Alan J. McKane

This paper quantifies the ergodicity and the rate of decay of the tail of the stationary distribution for a broad class of storage models, encompassing constant, linear, and power-type release rates with both finite and infinite activity…

Probability · Mathematics 2025-11-19 Miha Brešar , Aleksandar Mijatović , Nikola Sandrić

This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $\beta$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the…

Probability · Mathematics 2024-09-26 Yutao Ma , Siyu Wang

In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Log Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape…

Methodology · Statistics 2014-01-16 Frederico Caeiro , Dora Prata Gomes

A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…

Probability · Mathematics 2020-12-07 Dawid Czapla , Katarzyna Horbacz , Hanna Wojewódka-Ściążko