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Pareto Lévy measures and multivariate regular variation. (English) Zbl 1248.60052
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.

##### MSC:
 60G51 Processes with independent increments; Lévy processes 60E07 Infinitely divisible distributions; stable distributions 60G52 Stable stochastic processes 60G70 Extreme value theory; extremal stochastic processes 62H05 Characterization and structure theory for multivariate probability distributions; copulas
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