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Topological regular variation: III. Regular variation [PDF]
Topology and its Applications, 2010 The paper extends the topological theory of regular variation of the slowly varying case of \textit{N. H. Bingham} and \textit{A. J. Ostaszewski} [Topology Appl. 157, No. 13, 1999--2013 (2010; Zbl 1202.26004)] to the regularly varying functions between metric groups, viewed as normed groups, cf. \textit{N. H. Bingham} and \textit{A. J.
Bingham, N.H., Ostaszewski, A.J.
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Regular variation of GARCH processes [PDF]
Stochastic Processes and their Applications, 2002 We show that the finite-dimensional distributions of a GARCH process are regularly varying, i.e., the tails of these distributions are Pareto-like and hence heavy-tailed. Regular variation of the joint distributions provides insight into the moment properties of the process as well as the dependence structure between neighboring observations when both ...
Basrak, Bojan +2 more
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Topological regular variation: I. Slow variation [PDF]
Topology and its Applications, 2010 The authors extend and unify the multivariate regular variation literature by a reformulation in the language of topological dynamics. They use metric groups and study convergence and divergence of self-homeomorphisms in a normed topological group. The authors define a general form of slow variation on a metric space \(S\) that includes and extends ...
Bingham, N.H., Ostaszewski, A.J.
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From extended regular variation to regular variation with application in extreme value statistics [PDF]
Journal of Mathematical Analysis and Applications, 2009 This paper offers a unified treatment of the asymptotic properties for most estimators of extreme value characteristics to be found in the literature. A relation between regular variation and extended regular variation of second order is established. The study is organized in five sections, the first two preparing the background necessary for the proof
Neves, Cláudia
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Testing the multivariate regular variation model [PDF]
, 2021 In this paper, we propose a test for the multivariate regular variation model. The test is based on testing whether the extreme value indices of the radial component conditional on the angular component falling in different subsets are the same ...
Zhou, Chen +3 more
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On regular variation of entire Dirichlet series
Математичні Студії, 2023 Consider an entire (absolutely convergent in $\mathbb{C}$) Dirichlet series $F$ with the exponents $\lambda_n$, i.e., of the form $F(s)=\sum_{n=0}^\infty a_ne^{s\lambda_n}$, and, for all $\sigma\in\mathbb{R}$, put $\mu(\sigma,F)=\max\{|a_n|e^{\sigma ...
P. V. Filevych, O. B. Hrybel
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Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We are interested in the structure of the solution space of second-order half-linear differential equations taking into account various classifications regarding asymptotics of solutions.
Pavel Řehák
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Large noise in variational regularization [PDF]
Transactions of Mathematics and Its Applications, 2018 Abstract In this paper we consider variational regularization methods for inverse problems with large noise that is in general unbounded in the image space of the forward operator. We introduce a Banach space setting that allows to define a reasonable notion of solutions for more general noise in a larger space provided that one has ...
Burger, Martin +2 more
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Tail measures and regular variation
Electronic Journal of Probability, 2022 37 pages ...
Bladt, Martin +2 more
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Second order corrections for the limits of normalized ruin times in the presence of heavy tails
Stochastic Systems, 2014 In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [4] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In this paper
Dominik Kortschak, Søren Asmussen
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