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A characterization of multivariate regular variation [PDF]
Annals of Applied Probability, 2002 We establish the equivalence between the multivariate regular variation of a random vector and the univariate regular variation of all linear combinations of the components of such a vector.
, Bojan Basrak, Thomas Mikosch
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Sparse regular variation [PDF]
Advances in Applied Probability, 2021 AbstractRegular variation provides a convenient theoretical framework for studying large events. In the multivariate setting, the spectral measure characterizes the dependence structure of the extremes. This measure gathers information on the localization of extreme events and often has sparse support since severe events do not simultaneously occur in ...
Meyer, Nicolas, Wintenberger, Olivier
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Models with Hidden Regular Variation: Generation and Detection
Stochastic Systems, 2015 We review the notions of multivariate regular variation (MRV) and hidden regular variation (HRV) for distributions of random vectors and then discuss methods for generating models exhibiting both properties concentrating on the non-negative orthant in ...
Sidney Resnick, Bikramjit Das
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A Seneta's Conjecture and the Williamson Transform [PDF]
Sahand Communications in Mathematical Analysis, 2023 Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$
Edward Omey, Meitner Cadena
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Extremes and Regular Variation [PDF]
, 2021 We survey the connections between extreme-value theory and regular variation, in one and higher dimensions, from the algebraic point of view of our recent work on Popa groups.
Bingham, N. H., Ostaszewski, A. J.
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Truncated Moments for Heavy-Tailed and Related Distribution Classes
Mathematics, 2023 Suppose that ξ+ is the positive part of a random variable defined on the probability space (Ω,F,P) with the distribution function Fξ. When the moment Eξ+p of order p>0 is finite, then the truncated moment F¯ξ,p(x)=min1,Eξp1I{ξ>x}, defined for all x⩾0, is
Saulius Paukštys +2 more
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Bias Reduction in Variational Regularization [PDF]
Journal of Mathematical Imaging and Vision, 2017 Accepted by ...
Eva-Maria Brinkmann +3 more
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Polynomial tails of additive-type recursions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Polynomial bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees, or in recursive algorithms.
Eva-Maria Schopp
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REGULAR VARIATION AND SMILE ASYMPTOTICS [PDF]
Mathematical Finance, 2009 We consider risk‐neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results.
Benaim, S., Friz, P.
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Even Order Half-Linear Differential Equations with Regularly Varying Coefficients
Mathematics, 2020 We establish nonoscillation criterion for the even order half-linear differential equation (−1)nfn(t)Φx(n)(n)+∑l=1n(−1)n−lβn−lfn−l(t)Φx(n−l)(n−l)=0, where β0,β1,…,βn−1 are real numbers, n∈N, Φ(s)=sp−1sgns for s∈R, p∈(1,∞) and fn−l is a regularly varying (
Vojtěch Růžička
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