Extreme Value Theory: Theory, Methodology and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 848

Special Issue Editor


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Guest Editor
Department of Mathematics and Statistics, University of North Carolina—Wilmington, Wilmington, NC 28403, USA
Interests: discrete probability; hidden truncation probability models and associated inference; financial risk modeling via copula; copula based construction of multivariate probability distributions and associated inference; bayesian inference; nonparametric regression; survival data analysis; reliability theory; near-compatibility of discrete probability distributions via divergence measures; inference based on order statistics; distribution theory; classical and bayesian inference; financial risk modeling; order statistics; copula based construction of bivariate and multivariate distributions and associated inference; copula-based dependence measures; probability theory and stochastic process; risk assessment

Special Issue Information

Dear Colleagues,

Extreme Values arising out of univariate, bivariate, and multivariate random variables, as well as through stochastic processes, have soared to prominence over recent decades, being notably spurred on by a climate emergency, among other elements. Regular Variation theory not only lies at the centre of classical Extreme Value theory, but it also continues to steadily underpin significant advances in statistical inference for tail-related data and connected empirical processes.

This Special Issue aims to celebrate, explore and disseminate the latest research taking place within the realms of Extreme Values, examining new advancements in terms of theory, methodology, Regular Variation and Empirical Processes, including research developed at the interface of Extremes (broadly understood) with applied sciences at large. High-quality research contributions describing original, innovative, empirical, or scoping out-type unpublished work in the above-named areas, also mirrored in the following keywords, are cordially invited for publication:

spatial and/or temporal processes; methodological statistics; nonparametric statistic machine learning; causal inference; regression models; applied probability; graphical models; optimization; data science; applied statistical modelling and simulation.

Dr. Indranil Ghosh
Guest Editor

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Keywords

  • spatial and/or temporal process
  • methodological statistics
  • nonparametric statistics machine learning
  • causal inference
  • regression models
  • applied probability
  • graphical models
  • optimization
  • data science
  • applied statistical modelling and simulation

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Published Papers (1 paper)

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Research

11 pages, 262 KiB  
Article
On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications
by Azam A. Imomov, Erkin E. Tukhtaev and János Sztrik
Mathematics 2024, 12(20), 3266; https://doi.org/10.3390/math12203266 - 18 Oct 2024
Viewed by 543
Abstract
In this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with a remainder depending on the [...] Read more.
In this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with a remainder depending on the types of remainder. We also prove several important theorems on the asymptotic representation of integrals of Karamata functions. Under certain conditions, we observe a “narrowing” of classes of slowly varying functions concerning the types of remainder. At the end of the paper, we discuss the possibilities of the application of slowly varying functions in the theory of stochastic branching systems. In particular, under the condition of the finiteness of the moment of the type Exlnx for the particle transformation intensity, it is established that the property of slow variation with a remainder is implicitly present in the asymptotic structure of a non-critical Markov branching random system. Full article
(This article belongs to the Special Issue Extreme Value Theory: Theory, Methodology and Applications)
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