Results 1 to 10 of about 40,557 (254)
Multivariate Regular Variation of Preferential Attachment Models [PDF]
, 2023 We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in time and treat the incoming edge count of all existing nodes as a random vector of random length.
Anja Janßen, Max Ziegenbalg
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A characterization of multivariate regular variation [PDF]
The 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 +2 more
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Operator Regular Variation of Multivariate Liouville Distributions [PDF]
, 2023 Operator regular variation reveals general power-law distribution tail decay phenomena using operator scaling, that includes multivariate regular variation with scalar scaling as a special case. In this paper, we show that a multivariate Liouville distribution is operator regularly varying if its driving function is univariate regularly varying.
Haijun Li
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Marginal expected shortfall inference under multivariate regular variation [PDF]
, 2023 Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context, results of statistical inference rely on the bivariate extreme values approach, disregarding the extremal dependence ...
Simone A. Padoan +2 more
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Pareto Lévy Measures and Multivariate Regular Variation [PDF]
Advances in Applied Probability, 2012 We consider regular variation of a Lévy processX:= (Xt)t≥0inwith Lévy measure Π, emphasizing the dependence between jumps of its components. By transforming the one-dimensional marginal Lévy measures to those of a standard 1-stable Lévy process, we decouple the marginal Lévy measures from the dependence structure.
Irmingard Eder, Claudia Klüppelberg
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Multivariate regular variation of heavy-tailed Markov chains [PDF]
, 2007 The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is allowed to switch from positive to negative extremes or vice versa, the distribution of the tail chain increment ...
Johan Segers
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Testing the Multivariate Regular Variation Model [PDF]
SSRN Electronic Journal, 2018 In this article, we propose a test for the multivariate regular variation (MRV) 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.
J.H.J. Einmahl, Fan Yang, Chen Zhou
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FunctionaL Regular Variation of L\\'evy-driven Multivariate Mixed Moving\n Average Processes [PDF]
, 2012 We consider the functional regular variation in the space $\mathbb{D}$ of c dl g functions of multivariate mixed moving average (MMA) processes of the type $X_t = \int\int f(A, t - s) (d A, d s)$. We give sufficient conditions for an MMA process $(X_t)$ to have c dl g sample paths. As our main result, we prove that $(X_t)$ is regularly varying in
Robert Stelzer, Martin Moser
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Generation and Detection of Multivariate Regular Variation and Hidden Regular Variation [PDF]
, 2014 We review definitions of multivariate regular variation (MRV) and hidden regular variation (HRV) for distributions of random vectors and then summarize methods for generating models exhibiting both properties. We also discuss diagnostic techniques that detect these properties in multivariate data and indicate when models exhibiting both MRV and HRV are
Bikramjit Das, Sidney I. Resnick
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Diversification Benefits Under Multivariate Second Order Regular Variation [PDF]
SSRN Electronic Journal, 2017 We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk .
Bikramjit Das, Marie Kratz
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