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We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…

Probability · Mathematics 2016-05-10 Anja Janßen , Thomas Mikosch , Mohsen Rezapour , Xiaolei Xie

Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…

Probability · Mathematics 2023-01-11 Günter Last

We show that the set of $d$-variate symmetric stable tail dependence functions, uniquely associated with exchangeable $d$-dimensional extreme-value copulas, is a simplex and determine its extremal boundary. The subset of elements which…

Statistics Theory · Mathematics 2020-12-11 Jan-Frederik Mai , Matthias Scherer

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

Methodology · Statistics 2015-02-26 Rafał Kulik , Zhigang Tong

The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…

Methodology · Statistics 2020-09-15 Raphaël Huser , Jennifer L. Wadsworth

This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…

General Mathematics · Mathematics 2025-07-08 Sergei Rogosin , Filippo Giraldi , Francesco Mainardi

Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…

Methodology · Statistics 2026-04-15 Mirco Lescart , Anna Kiriliouk , Philippe Naveau

We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail…

Probability · Mathematics 2012-03-09 Helena Ferreira

We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.

Probability · Mathematics 2019-07-03 Denis Denisov , Elena Perfilev , Vitali Wachtel

The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…

Probability · Mathematics 2021-03-31 Philippe Soulier

We consider the random variables $R$ which are solutions of the distributional equation $R\overset{\cL}{=}MR+Q$, where $(Q,M)$ is independent of $R$ and $\ABS{M}\leq 1$. Goldie and Gr\"ubel showed that the tails of $R$ are no heavier than…

Probability · Mathematics 2009-12-23 Jean-Baptiste Bardet , Hélène Guerin , Florent Malrieu

This paper states asymptotic equivalents for the three first moments of the Eescher transform of a distribution on R with smooth density in the upper tail. As a by product if provides a tail approximation for its moment generating function,…

Statistics Theory · Mathematics 2014-03-21 Maeva Biret , Michel Broniatowski , Zhansheng Cao

We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…

Mathematical Physics · Physics 2022-01-05 Hiroshi Horii , Raphael Lefevere , Takahiro Nemoto

The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan \emph{et al.} allows to also account for asymptotic independence. In this paper we introduce…

Statistics Theory · Mathematics 2012-10-30 Helena Ferreira , Marta Ferreira

This paper demonstrates that, under a particular convention, the convex functions that characterise the phi divergences also generate Archimedean copulas in at least two dimensions. As a special case, we develop the family of Archimedean…

Methodology · Statistics 2025-10-08 Alan R. Pearse , Howard Bondell

The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…

Probability · Mathematics 2019-07-23 Pavlina Jordanova

We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…

Classical Analysis and ODEs · Mathematics 2025-12-11 Ikki Fukuda , Yoshiki Kagaya , Yuki Ueda

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we…

Statistics Theory · Mathematics 2012-12-11 Marta Ferreira , Helena Ferreira

In this paper, we focus on stochastic comparisons of extreme order statistics stemming from multiple-outlier scale models with dependence. Archimedean copula is used to model dependence structure among nonnegative random variables.…

Statistics Theory · Mathematics 2020-12-16 Sangita Das , Suchandan Kayal

While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present challenges when Gaussian-based variational inference fails to capture tail decay accurately. We first…

Machine Learning · Statistics 2022-05-18 Feynman Liang , Liam Hodgkinson , Michael W. Mahoney