Pareto Lévy measures and multivariate regular variation (Q2879909)
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scientific article; zbMATH DE number 6022666
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pareto Lévy measures and multivariate regular variation |
scientific article; zbMATH DE number 6022666 |
Statements
10 April 2012
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multivariate Lévy processes
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Pareto--Lévy copula
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Lévy measure
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multivariate regular variation
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multivariate stable processes
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spectral measure
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tail integral
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tail dependence coefficient
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Pareto Lévy measures and multivariate regular variation (English)
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The authors consider regular variation of an \(\mathbb R^d\)-valued Lévy process \(X\) with Lévy measure \(\Pi\), emphasizing the dependence between jumps of its components. By transforming the marginal Lévy measures to those of a standard \(1\)-stable Lévy process, they decouple the marginal Lévy measure from the dependence structure. The dependence between the jumps is modeled by the so-called Pareto Lévy measure. The authors characterize the multivariate regular variation of \(X\) by its one-dimensional marginal Lévy measures and the Pareto Lévy measure.
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